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Tóm tắt nội dung (trích từ tài liệu gốc): Cognitive Systems Monographs Volume 2 Editors: R�diger Dillmann � Yoshihiko Nakamura � Stefan Schaal � David Vernon Tijana T. Ivancevic, Bojan Jovanovic, Swetta Djukic, Milorad Djukic, and Sasa Markovic Complex Sports Biodynamics With Practical Applications in Tennis BA C R�diger Dillmann, University of Karlsruhe, Faculty of Informatics, Institute of Anthropomatics, Robotics Lab., Kaiserstr. 12, 76128 Karlsruhe, Germany Yoshihiko Nakamura, Tokyo University Fac. Engineering, Dept. Mechano-Informatics, 7-3-1 Hongo, Bukyo-ku Tokyo, 113-8656, Japan Stefan Schaal, University of Southern California,

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Cognitive Systems Monographs



Volume 2



Editors: R�diger Dillmann � Yoshihiko Nakamura � Stefan Schaal � David Vernon

Tijana T. Ivancevic, Bojan Jovanovic,

Swetta Djukic, Milorad Djukic,

and Sasa Markovic



Complex Sports

Biodynamics



With Practical Applications in Tennis



BA C

R�diger Dillmann, University of Karlsruhe, Faculty of Informatics, Institute of Anthropomatics,

Robotics Lab., Kaiserstr. 12, 76128 Karlsruhe, Germany



Yoshihiko Nakamura, Tokyo University Fac. Engineering, Dept. Mechano-Informatics, 7-3-1 Hongo,

Bukyo-ku Tokyo, 113-8656, Japan



Stefan Schaal, University of Southern California, Department Computer Science, Computational Learn-

ing & Motor Control Lab., Los Angeles, CA 90089-2905, USA



David Vernon, Khalifa University Department of Computer Engineering, PO Box 573, Sharjah, United

Arab Emirates



Authors                                   Mr. Swetta Djukic



Dr. Tijana Ivancevic                      Trinity Gardens Tennis Club Inc.

                                          18 Tatiara Grove, Rostrevor

School of Electrical and Information      South Australia, 5073, Australia

Engineering, Division of

Information Technology &                  Dr. Milorad Djukic

Engineering and the Environment

University of South Australia             Univerzitet u Novom Sadu

Mawson Lakes Boulevard                    Fakultet fizicke kulture

Mawson Lakes, S.A. 5095                   Lovcenska 16

Australia                                 21000 Novi Sad, Serbia



Mr. Bojan Jovanovic                       Dr. Sasa Markovic



Fruskogorska 30/143                       Univerzitet u Nisu

21000 Novi Sad                            Fakultet sporta i fizickog vaspitanja

Serbia                                    Carnojevica 10a

                                          18000 Nis, Serbia

ISBN 978-3-540-89970-9

                                           e-ISBN 978-3-540-89971-6

DOI 10.1007/978-3-540-89971-6



Cognitive Systems Monographs              ISSN 1867-4925



Library of Congress Control Number: 2008942040



c 2009 Springer-Verlag Berlin Heidelberg



This work is subject to copyright. All rights are reserved, whether the whole or part of the material is

concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,

reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication

or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,

1965, in its current version, and permission for use must always be obtained from Springer. Violations

are liable for prosecution under the German Copyright Law.



The use of general descriptive names, registered names, trademarks, etc. in this publication does not

imply, even in the absence of a specific statement, that such names are exempt from the relevant protective

laws and regulations and therefore free for general use.



Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India.



Printed in acid-free paper



543210



springer.com

Preface



What are motor abilities of Olympic champions? What are essential psycho-

logical characteristics of Mark Spitz, Carl Lewis and Roger Federer? How

to discover and maximally develop motor intelligence? How to develop in-

domitable will power of Olympic champions? What are the secrets of selec-

tion for the future Olympic champions? Does for every sport exist a unique

model of an Olympic champion? This book gives a modern scientific answers

to the above questions. Its purpose is to give you the answer to everything

you ever wanted to ask about sport champions, but didn't know who or how

to ask.



   In particular, the purpose of this book is to give you the answer to every-

thing you ever wanted to ask about advanced tennis, but didn't know who or

how to ask. Its aim is to dispel classical myths of a "biomechanically sound"

serve, forehand, and backhand, as well as provide methods for developing

superior tennis weapons, a lightning�fast game, and unrivaled mental speed

and strength � essential qualities of a future tennis champion.



   This book does not describe a method that was used by Sampras, or Borg,

or any other great tennis champion from the past. Nor does it explain current

tennis basics as so many other books do. This book takes a totally different

perspective, it describes and explains the physical and mental abilities of a

champion in future tennis. Weapons of a future tennis game will comprise of

whip�like tennis serves and strokes, based on the stretch�reflex, and using

the whole body in a fluid and integrated manner, thus manifesting a superb

combination of speed and strength. To ensure that these weapons will per-

form consistently, and under all possible circumstances, phenomenal mental

strength and speed are also needed.



   Now, full appreciation should be given to the current world number one,

Roger Federer. He is the present model of a champion (especially when com-

bined with Nadal and Djokovic). Regarding the future tennis champion model

that will be outlined in this book, this Federer�model will be taken as a ba-

sis: all his abilities, both physical and mental, both technical and tactical,

even including his body height and weight. This Federer�model will just be

VI                      Preface



empowered with tremendously�strong muscles and lightning�fast reflexes,

giving him a 300+ km/h serve, a 240+ km/h forehand and a 200+ km/h back-

hand, together with a visual perception and complex reaction quick enough to

anticipate and follow the bullet�like ball generated by the mentioned strokes,

with Federer's concentration and anticipation of the opponent.



   By combining ex�Russian sport science with today's American wealth and

technology, future tennis world champions could easily be produced.



   Think! Don't be constrained by anyone. Sport is a science not a religion.

Learn the facts, apply the knowledge and believe in your unlimited potential

and you can become a tennis champion. Producing a sport champion is a

joy, satisfaction and fulfilment; not frustration and suffering. A brain also is

needed to complete a tennis champion: a strong & fast brain would make

strong & fast muscles invincible.



   This myth�buster book gives modern scientific answers to all the questions

that must have arisen in your head after reading the past few paragraphs.

The book includes 12 chapters on various topics related to complex sports

biodynamics, a strong list of references on sports science in general and tennis

in particular, as well as a comprehensive index. To make the book more

readable for the widest possible audience, the last Chapter on tennis has

been written in a popular (non-rigorous) question & answer format.



   Tijana Ivancevic, Ph.D. in Applied Mathematics and Master of Sports

Biomechanics, is a co-author of 10 advanced, biomechanics�related, scientific

monographs (seven of them published with Springer and three with World

Scientific). She is currently working as a Senior Researcher in mathematical

modelling in medicine at the University of South Australia. Previously, she

developed breast�cancer classifiers based on a differential geometry of neural

networks at the University of Adelaide. Tijana has also worked on various

artificial/computational intelligence projects, as well as neural networks ap-

plications to sports science and biomechanics. Bojan Jovanovic is currently

developing a biomechanical dynamics simulator at the University of Novi

Sad, for sport games in general, handball in particular. Swetta Djukic has

over thirty years of experience in competitive tennis and in 2006 was awarded

as an undefeated senior tennis player at the famous Trinity Gardens Tennis

Club. Milorad Djukic is an Associate Professor of Handball at the Univer-

sity of Novi Sad and the Chair of Technical Committee of of the handball

club Vojvodina. Sasa Markovic is an Associate Professor of Handball at the

University of Nis and the President of the Handball Coaches Association of

Serbia.



Adelaide, October 2008  Tijana T. Ivancevic

                            Bojan Jovanovic

                               Swetta Djukic

                             Milorad Djukic

                              Sasa Markovic

Contents



1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 CSB-Physics and Metaphysics . . . . . . . . . . . . . . . . . . . . . . . . . . 5



      2.1 Qualitative CSB and Standard Physical Theory . . . . . . . . . . . 7

            2.1.1 Poincar�e's Qualitative Dynamics . . . . . . . . . . . . . . . . . . 7

            2.1.2 Poincar�e's Point of View: Phase�Portrait . . . . . . . . . . . 7

            2.1.3 Standard Description of a Physical Theory . . . . . . . . . 9



3 CSB-Structure and Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

      3.1 Basic Input�Output CSB-System . . . . . . . . . . . . . . . . . . . . . . 11

      3.2 Example of a `Pure CSB-System': Human Skeletal

            Muscle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

      3.3 Example of an `Applied CSB-System': Sprint Velocity

            Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20



4 CSB-Biomechanics: Structure and Function of Human

      Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

      4.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

      4.2 Group Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

      4.3 Hamiltonian Biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

      4.4 Muscular Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

            4.4.1 Elements of Muscular Histology . . . . . . . . . . . . . . . . . . . 30

            4.4.2 Huxley's Sliding�Filaments Dynamics . . . . . . . . . . . . . . 32

            4.4.3 Hill's Force�Velocity (Thermo)Dynamics . . . . . . . . . . . 33

            4.4.4 Basic Musculo�Skeletal Dynamics . . . . . . . . . . . . . . . . . 34

      4.5 Stretch Reflex and Motor Servo . . . . . . . . . . . . . . . . . . . . . . . . . 36

      4.6 Cerebellar Movement Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

      4.7 Closing the (Bio)Mechanical Circle . . . . . . . . . . . . . . . . . . . . . . 45

      4.8 Biomechanical Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

      4.9 Estimation of Musculo�Skeletal Parameters . . . . . . . . . . . . . . . 49

VIII  Contents



            4.9.1 Measurement of Muscular Input Torqes . . . . . . . . . . . . 49

            4.9.2 Measurement of Skeleton and Joint Parameters . . . . . 50

            4.9.3 Testing of Model Outputs . . . . . . . . . . . . . . . . . . . . . . . . 50

            4.9.4 Further Analysis of Model Outputs . . . . . . . . . . . . . . . . 51

      4.10 Stochastic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51



5 CSB-System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

      5.1 Linear CSB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

      5.2 Functional CSB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

      5.3 Nonlinear CSB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

      5.4 CSB-Cognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62



6 CSB-Synergetics: Escape from Chaos . . . . . . . . . . . . . . . . . . 69

      6.1 Biomechanical Chaos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

      6.2 Basic Principles of Synergetics . . . . . . . . . . . . . . . . . . . . . . . . . . 70

      6.3 Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

      6.4 Order Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

      6.5 Macroscopic Biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

      6.6 Control of the Biomechanical Chaos . . . . . . . . . . . . . . . . . . . . . 76



7 CSB-Subsystems: Energy and Information Flows . . . . . . . 79

      7.1 CSB-Energy Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

            7.1.1 The Immediate Energy Source . . . . . . . . . . . . . . . . . . . . 79

            7.1.2 The Principle of Coupled Reactions . . . . . . . . . . . . . . . . 79

            7.1.3 AT P - P C: The Phosphagen System . . . . . . . . . . . . . . 80

            7.1.4 The Lactic Acid System . . . . . . . . . . . . . . . . . . . . . . . . . . 80

            7.1.5 The Oxygen, or Aerobic, System . . . . . . . . . . . . . . . . . . 81

            7.1.6 The Energy Continuum Concept . . . . . . . . . . . . . . . . . . 82

      7.2 CSB-Information Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

            7.2.1 CSB-Motor Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

            7.2.2 CSB-Adaptive Filtration . . . . . . . . . . . . . . . . . . . . . . . . 84



8 Neuro-CSB: Artificial Neural Networks . . . . . . . . . . . . . . . . 87

      8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

      8.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

      8.3 Backpropagation of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

            8.3.1 Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

            8.3.2 Recall � Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

      8.4 Hopfield Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

      8.5 CSB-Neurodynamics: The Cerebellum . . . . . . . . . . . . . . . . . . 97



9 CSB-Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

      9.1 Human Mind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

      9.2 Human Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

            9.2.1 Psychometric Definition of Intelligence . . . . . . . . . . . . . 145

            9.2.2 Correlation and Factor Analysis . . . . . . . . . . . . . . . . . . . 149

            9.2.3 Cognitive Versus Not�Cognitive Intelligence . . . . . . . . 173

Contents  IX



            9.2.4 Intelligence and Cognitive Development . . . . . . . . . . . . 175

            9.2.5 Psychophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

            9.2.6 Human Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . 185

            9.2.7 Human Mind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

            9.2.8 The Mind�Body Problem . . . . . . . . . . . . . . . . . . . . . . . . . 197

            9.2.9 Analytical Psychology . . . . . . . . . . . . . . . . . . . . . . . . . . . 209



10 Smart CSB-Agents for Games Modelling . . . . . . . . . . . . . . . 215

      10.1 CSB-Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

      10.2 Types of CSB-Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

            10.2.1 Deliberate Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

            10.2.2 Reactive Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

            10.2.3 Hybrid Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

      10.3 CSB-Agents' Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

      10.4 CSB-Agents' Reasoning and Learning . . . . . . . . . . . . . . . . . . 224

            10.4.1 Reasoning and Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 224

            10.4.2 Rational Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225



11 Psycho-CSB: Mental Concentration in Sport . . . . . . . . . . . 229

      11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

      11.2 Concentration in Sport: Experiences of Top Athletes . . . . . . . 231

      11.3 Concentration Exercises for Training and Competition . . . . . 232

      11.4 Inspiration and Enthusiasm, Discipline and Progress . . . . . . . 232



12 Tennis Champion of the Future . . . . . . . . . . . . . . . . . . . . . . . . . . 235

      12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

      12.2 Contemporary Tennis Science . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

            12.2.1 Tennis Muscles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

            12.2.2 Tennis Anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

            12.2.3 Tennis Energetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

            12.2.4 Tennis Biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

            12.2.5 Motor Control in Tennis . . . . . . . . . . . . . . . . . . . . . . . . . 255

            12.2.6 Tennis Psychology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

      12.3 Tennis Science of the Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

            12.3.1 High Performance in Tennis . . . . . . . . . . . . . . . . . . . . . . 266

            12.3.2 Athleticism in Tennis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

            12.3.3 Muscular Slingshots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

            12.3.4 The Biomechanics of Whip�Like Movements . . . . . . . . 281

            12.3.5 Superior Tennis Weapons . . . . . . . . . . . . . . . . . . . . . . . . 282

            12.3.6 Mental Training in Tennis . . . . . . . . . . . . . . . . . . . . . . . . 285

            12.3.7 Tennis Chess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

            12.3.8 The Tennis Champion of the Future . . . . . . . . . . . . . . . 291

      12.4 A Fuzzy�Logic Tennis Simulator . . . . . . . . . . . . . . . . . . . . . . . . 293



References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299



Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

Acknowledgements



We wish to express our deepest gratitude to Dr. Vladimir Ivancevic, the

world leader in human biodynamics, for his support and advice. We would

also like to thank our families for their love and support through the process

of book-making, especially Nick and Atma Ivancevic, with their help in the

chapter describing tennis chess; and Natalia Djukic, with her help in editing

references. Finally, we would like to express special thanks to the Springer

Editors, Dr. Thomas Ditzinger and Dr. Dieter Merkle.

Chapter 1



Introduction



Complex Sport Biodynamics (CSB, for short) is a new kind of sport science,

the Know�How to make sport champions. CSB combines the essential prin-

ciples of complex systems dynamics [II06b, B-Y97], biomechanics, [II05], bio-

dynamics and sports physiology [II06a, Mar98, GM88], chaos theory [II07a],

neurophysiology [II07b] and computational psychodynamics [IA07, II07c] �

with a unique goal : the SUPREME SPORT RESULT.1



   This unique goal is in CSB represented by the two essential CSB tasks

(see Figure 1.1)



1. Direct�training task : given the set of empirically proclaimed talents -

   develop the champion model



2. Inverse�selection task : given the champion model - develop the talent

   model



   In CSB all the champions are represented by the champion model for a par-

ticular discipline, and all the talents are represented by the talent model for the

same discipline. In language of `factor analysis' (see below), both the champion

and the talent have the same factor structure � only it is fully developed in case

of the champion and yet undeveloped in case of the talent. These general rep-

resentatives are usually some heuristic combinations of causal�system models,

empirical�expert models, and statistical�factor models.



   Both essential problems are solvable by certain combination of the three

basic CSB�methods:



1. mathematical modelling, control, and learning;

2. computer simulations and animations; and

3. mental concentration and meditation.



   The direct problem is called CSB�learning or training process. The in-

verse problem is called CSB�recognition or selection process. Theoretically



 1 The goal of CSB is the SUPREME SPORT RESULT � the `Olympic Gold', or the

    `Grand Slam', without drugs, without anything `unhealthy' and without any kind of

    `cheating', which is all, unfortunately, so much present in a nowadays sport.



T.T. Ivancevic et al.: Complex Sports Biodynamics, COSMOS 2, pp. 1�4.



springerlink.com  c Springer-Verlag Berlin Heidelberg 2009

2  1 Introduction



Fig. 1.1 Two main recursive CSB-tasks. A talent is a child with the same basic

pattern�structure as a champion. Training dynamics is a pair of nonlinear trans-

forms between patterns of talent and champion: (i) Direct, continuous training flow

= evolution of the talent pattern into the champion pattern, and (ii) Inverse, dis-

crete selection map = recognition of the champion pattern inside the talent pattern.



speaking, the inverse problem can be solved much easier, because the model

of the talent (by definition) has all the components as the model of the cham-

pion, but in a non�developed form of potentials. And the direct problem is

in fact how to use all CSB engines in developing the potentials of the talent,

to make him the champion.



   The kernel of the CSB�method is the mathematical structure called map-

ping, or map (Figure 1.2), i.e., a correspondence between two abstract sets

(see [AM78]). It is said that the mapping f maps the original set X (do-

main) into the image set Y (range, or codomain), denoted by f : X  Y ,

if there is a correspondence of elements x1, x2, . . . , xn from X with elements

y1, y2, . . . , ym from Y .



   For the existence of the inverse mapping f -1 (in which the set Y becomes the

original one and the set X the image one) the necessary and sufficient condi-

tion is that the direct mapping f is bijective, i.e., (i) surjective (if each element

from Y is the image of a certain element from X), and (ii) injective (if different

elements from X are mapped into different elements from Y ) simultaneously.



   If X and Y represent sets of real numbers, a mapping f : X  Y is usually

called a function. One�dimensional function is represented by a curve (Figure

1.3) in an Euclidean plane. Two�dimensional function is represented by a

surface in 3D Euclidean space, and N -dimensional function is represented

by a hypersurface in N -dimensional Euclidean space. For the existence of all

the image elements y1, y2, . . . , ym (distributed along the set Y ) it is necessary

that the curve (respectively surface, or hypersurface) f is continuous. And

for the uniqueness of the image elements y1, y2, . . . , ym it is necessary that f

is continuous and smooth.

1 Introduction          3



Fig. 1.2 The kernel of

the CSB�method



Fig. 1.3 One�

dimensional function



   In the system language, f is called the feedforward path, and f -1 is called

the feedback path.



   In the functional language, the CSB-goal is represented by the pair of

mappings (f, f -1), where f represents the direct problem of CSB-training,

and f -1 represents the inverse problem of CSB-selection.



   Thus, sports science is all about training methods (directed to make a

champion) and selection methods (directed to finding talents). In sports

science all the champions are represented by the champion model for a partic-

ular discipline (e.g., tennis), and all the talents are represented by the talent

model for the same discipline (see Figure 1.1). In statistical language, both

the champion and the talent have the same factor structure � only it is fully

developed in case of the champion and yet undeveloped in case of the talent.

4  1 Introduction



   For example, on the current tennis circuit, Nadal, Roddick, Federer, and

Djokovic had all been talents. However, so far only one of them has proved

to be a real champion � Roger Federer, the man who apparently defies all

tennis statistics.2 Today, in our opinion, the highest chances to become future

tennis champions have Nadal and Djokovic.



 2 For the tennis performance criteria we can use the 10 points of the standard tennis

    game statistics (in brackets are the current ranks of Roger Federer, the world number

    one, on October 22nd 2007, as given by AT P tennis.com):3



� Service game: (i) number of aces (4), (ii) 1st serve percentage (29), (iii) 1st serve points

    won (6), (iv) 2nd serve points won (1), (v) service games won (3), and (vi) break points

    saved (8).



� Return of service: (vii) points won returning 1st serve (4), (viii) points won returning

    2nd serve (17), (ix) break points converted (36), and (x) return games won (10).

Chapter 2



CSB-Physics and Metaphysics



More then three centuries ago, more precisely in 1686, Sir Isaac Newton, one

of the foundation�stones of human thought (see [AM78]), in his famous book

`Philosophiae Naturalis Principia Mathematica', stated the metaphysical and

physical basis of modern sciences, including CSB (in spite of the influences

of modern physics).



   Methodology of all sciences tries to solve two main problems: explanation

and prediction. The problem of explanation (or basic understanding of the

structure and function of the object in consideration) has been (more or less

successfully) solved by both natural and social sciences. But the problem of

prediction has been (in a limited range) solved only by the so�called `exact

sciences' with developed mathematical, measurement, and computer simula-

tion equipment.



   Any form of prediction in science is based on Newton's principle of causal-

ity. We can even say that the human thought apparatus is based on this

(meta)physical principle.



   Newton's principle of causality (Figure 2.1) states:

If the initial state (in any chosen initial time) of any CSB�system is known

(measured on the system S-axis), and if all the influences upon the sys-

tem considered are known from the initial time on (measured on the time

t-axis), then the future behavior of the system (its `destiny') is completely

determined.



   More precisely Newton's causality principle can be formulated thus:

If the law (i.e., the balance) of forces acting upon the system is known together

with its initial conditions, than the law of motion (or, generally, behavior)

can be obtained exactly (by solving, either analytically or numerically, the

system equations for the given initial conditions).



   For the sake of mathematical formulation of the causality principle Newton

invented (independently of a mathematician� philosopher G.F. Leibnitz) dif-

ferential and integral calculus. The basic geometric idea of differential calculus

consists of the limiting process which transforms bilocally (i.e., in two distinct

space and/or time points) defined classic vector quantity (representing some



T.T. Ivancevic et al.: Complex Sports Biodynamics, COSMOS 2, pp. 5�9.



springerlink.com  c Springer-Verlag Berlin Heidelberg 2009

6                    2 CSB-Physics and Metaphysics



Fig. 2.1 Newton's

causality principle



average force, velocity or acceleration) into unilocally defined tangent vector

(representing instant force, velocity or acceleration). The process of obtaining

the tangent vector in each point of a curve is called differentiation, while the

inverse process is called integration. Differentiation of the time�dependent

trajectory with respect to time gives the curve of velocity, and differentia-

tion of the later gives the curve of acceleration. Geometric construction of

the tangent vector in each point of the curve is the special case of construc-

tion of the tangent bundle on the smooth manifold (a smooth curve is a

one-dimensional smooth manifold, surface is two�dimensional, and so on).

The projection of the tangent bundle on the original manifold represents the

process of (indefinite) integration.



   Newton's crucial second law of motion (see [AM78]� [MR94]) says: the

force acting on any CSB�system is proportional to the time rate of change

of velocity of the system, and the proportionality constant is the measure of

inertia of the system. Simplifying this statement, we have: the force acting

upon the system is equal to the product of its mass and its acceleration.

Formally: F = ma = mv = mx�, where overdot denotes the time derivative

(i.e., tangent vector in the given point of the curve, or the time rate of change

of the quantity considered), F represents the force, m � the mass, a � the

acceleration, v � the velocity, and x � the position coordinate.



   This equation implies some frame of reference with respect to which the ac-

celeration a = v = x� is measured. It is a fact of experience that Newton's law of

motion expressed in this simple form gives results in close agreement with expe-

rience when, and only when, the coordinate axes are fixed relative to the average

position of the `fixed' stars moving with uniform linear velocity and without ro-

tation relative to the stars. In either case the frame of reference is referred to as

an inertial frame and corresponding coordinates as inertial coordinates.



   Newton's causality principle can be now reformulated as: if the law of

force F = F (t) is known together with the initial conditions x0 = x(0) and

v0 = v(0), then the solution of upper (differential) equation of motion gives

the law of motion x = x(t).

2.1 Qualitative CSB and Standard Physical Theory  7



   Now, let us say a few words about explanation, or basic understanding.

In its customary meaning, the word `to understand' means to form oneself a

clear image or a diagram of an object or process. No matter how paradox-

ically this sounds, modern physics (predominantly quantum theory) cannot

be understood in this way. One of its founders, P.A.M. Dirac, wrote in this

respect [Dir67]:



   "... The main object of physical science is not the provision of pictures,

but is the formulation of laws governing phenomena and the applications of

these laws to the discovery of new phenomena ..."



   In the case of microscopic phenomena no picture can be expected to exist

in the usual sense of the word `picture', by which is meant a model func-

tioning essentially on classical lines. One may, however, extend the meaning

of the word `picture' to include any way of looking at the fundamental laws

which makes their self�consistency obvious. With this extension, one may

gradually acquire a picture of microscopic phenomena by becoming familiar

with the laws of modern physics. In CSB we are not dealing with microscopic

phenomena, but the logic of life itself hides something similar to microscopic

objects and processes.



2.1 Qualitative CSB and Standard Physical Theory



According to modern sports biomechanics (see [Zat98, Zat02]) as well as gen-

eral biodynamics (see [II05, II06a, II06b]), a human moving subject carrying

an accelerometer represents a 3D dynamical system governed by the Newton

Second Law of Motion. Therefore, modern dynamical systems theory seems to

be the most appropriate theoretical background for short-time motion data ac-

quisition using 3�axial accelerometers. In the following text we give a `plain�

English' brief description of modern dynamical systems theory of Newtonian

mechanics.



2.1.1 Poincar�e's Qualitative Dynamics



2.1.2 Poincar�e's Point of View: Phase�Portrait



Poincar�e visualized a dynamical system as a vector�field (i.e., a field of vectors

resembling those in electromagnetism) on the system's phase�space, in which

a solution is a smooth curve tangent at each of its points to the vector based

at that point. His qualitative dynamics is based on geometrical properties of

the system's phase�portrait : the family of solution curves, which fill up the

entire phase�space. For questions such as stability, it is necessary to study

the entire phase�portrait, including the behavior of solutions for all values of

the time parameter. Thus it was essential to consider the entire phase�space

at once as a single geometric object [AM78, Arn89].

8  2 CSB-Physics and Metaphysics



   Doing so, Poincar�e found the prevailing mathematical model for mechanics

inadequate, for its underlying space was Euclidean (or, a domain of several

real variables), whereas for a mechanical problem with angular variables or

constraints, the phase�space might be a more general, nonlinear space, such

as a generalized cylinder. Thus the global view in the qualitative dynamics

led Poincar�e to the notion of a smooth manifold (or, a differentiable manifold )

as a mechanical phase�space.



   In mechanical systems, this manifold always has a special geometric struc-

ture pertaining to the occurrence of phase variables (coordinates and mo-

menta) in canonically conjugate pairs, called a symplectic structure. Thus

the new mathematical model for mechanics consists of a symplectic mani-

fold , together with a Hamiltonian vector field , or global system of first�order

differential equations preserving the symplectic structure.



   This model offers no natural system of coordinates. Indeed a manifold

admits a coordinate system only locally, so it is most efficient to use Cartan's

intrinsic calculus rather than conventional Newton's calculus in the analysis

of this model. By suppressing unnecessary coordinates the full generality of

the theory becomes evident.



Poincar�e's Method: Differential Topology



The second characteristic of Poincar�e's qualitative dynamics is the replace-

ment of analytical methods by differential�topological ones in the study of

the phase�portrait. For many questions, for example the stability of the solar

system, one is interested finally in qualitative information about the phase�

portrait. In earlier times, the only techniques available were analytical. By

obtaining a complete or approximate quantitative solution, qualitative or geo-

metric properties could be deduced. It was Poincar�e's idea to proceed directly

to qualitative information by qualitative, that is, geometric methods. Thus

Poincar�e, Birkhoff, Kolmogorov, Arnold and Moser show the existence of pe-

riodic solutions in the 3�body problem by applying differential�topological

theorems to the phase�portraits in addition to analytical methods. No an-

alytical description of these orbits has been given. In some cases the orbits

have been plotted approximately by computers, but the computer cannot

prove that these solutions are periodic [AM78].



Poincar�e's Problem: Structural Stability



A third aspect of the qualitative dynamics is a new question that emerges

in it, namely the problem of structural stability, the most comprehensive of

many different notions of stability. This problem, first posed by Andronov�

Pontriagin, asks: If a dynamical system X has a known phase portrait P , and

is then perturbed to a slightly different system X (for example, changing

the coefficients in its differential equation slightly), then is the new phase

portrait P close to P in some topological sense? This problem is of obvious

2.1 Qualitative CSB and Standard Physical Theory  9



importance, since in practice the qualitative information obtained for P is to

be applied not to X, but to some nearby system X , because the coefficients

of the equation may be determined experimentally or by an approximate

model and therefore approximately [AM78, Arn93].



2.1.3 Standard Description of a Physical Theory



Recall that the standard description of a physical theory, most clearly enunci-

ated by [Duh54], consists of an experimental domain, a mathematical model ,

and a conventional interpretation. The model, being a mathematical system,

embodies the logic, or axiomatization, of the theory. The interpretation is

an agreement connecting the parameters and therefore the conclusions of the

model and the observables in the experimental domain.



   Traditionally, the philosopher�scientists judge the usefulness of a theory

by the criterion of adequacy, that is, the verifiability of the predictions, or the

quality of the agreement between the interpreted conclusions of the model

and the data of the experimental domain. To this Duhem adds the criterion of

stability [AM78]. This criterion refers to the structural stability or continuity

of the predictions, or their adequacy, when the model is slightly perturbed.

The general applicability of this type of criterion has been suggested by Ren�e

Thom [Tho75].



   This stability concerns variation of the model only, the interpretation and

domain being fixed. Therefore, it concerns mainly the model, and is primar-

ily a mathematical or logical question. Certainly all of the various notions

of stability in qualitative mechanics and ordinary differential equations are

special cases of this notion, including Laplace's problem of the stability of the

solar system and structural stability, as well as Thom's stability of biological

systems.

Chapter 3



CSB-Structure and Function



3.1 Basic Input�Output CSB-System



The essential CSB object, mapping, corresponds to unilateral logical oper-

ation implication (i.e., If�Then conditional), while the bilateral implication

represents logical equivalence (i.e., biconditional, or bilateral equality). By

introducing the time factor into the logical implication we obtain the New-

tonian causal (i.e., cause and effect ) process in which the effect necessarily

follows the cause with some time delay. Behavior of all CSB�systems (with

the exception of the highest level processes of learning) belongs to the cate-

gory of causal processes.



   The essential structure of all CSB�systems (see Figure 3.1) consists of

the pair of mappings (f, f -1) between the set X of input signals (stimuli, or

excitations) and the set Y of output signals (responses, or reactions). Both

the direct mapping f , and the inverse mapping f -1 must be continuous and

smooth. The behavior of such a kernel�system represents a specific flow of

matter, energy and information, taking place in space and time.



   The beginning of the system approach in life�sciences is usually connected

with the name of Canadian biologist L. von Bertalanffy [Ber73], who intro-

duced the term `open system' in 1932. This open system continually commu-

nicates (i.e., interchanges matter, energy and information) with its surround-

ings by means of its metabolism i.e., the totality of processes of anabolism

(input assembling process) and catabolism (output disassembling process). In

the same year Walter Cannon considered `the wisdom of the body' as the abil-

ity of the organism to maintain the stability of its internal midst, while Claude

Bernard (see [Ber73]) introduced the term homeostasis to signify the ability

of the living organisms for automatic self�stabilization of its internal midst

in spite of various perturbations of their surroundings. From this time, the

homeostasis has been mainly concerned with processes of regulation associ-

ated with physical movement, energy flow and material concentrations in the

living systems. The term `feedback' was placed by Norbert Wiener [Wie48]

in 1948 in the foundation of cybernetics, the general science of control and



T.T. Ivancevic et al.: Complex Sports Biodynamics, COSMOS 2, pp. 11�22.



springerlink.com  c Springer-Verlag Berlin Heidelberg 2009



---

[Cuối tài liệu]

322                                   Index



fuzzy sets 227                        Hotelling's rule 156

                                      Hotelling's T�square distribution 156

G�odel's incompleteness theorem 205   Hotelling transform 156

Gauss�Bolyai�Lobachevsky space        human mind 105

                                      Human skeletal and face muscles 30

       128                            hybrid dynamics 52

Gaussian distribution 150             hyperbolic force�velocity curve 33

Gaussian function 151                 hyperbolic force-velocity 36

general cognitive ability 170         hyperbolic geometry 128

general intelligence 170

generalized accelerations 45          If�Then 11

generalized coordinates 45            image set 2

generalized forces 46                 imagination 192

generalized Kaplan�Yorke relation 78  imitation 114, 143

generalized momenta 46                implication 11

generalized Newton's equations of     index file 65

                                      inferior cerebellar peduncle 42, 100

       motion 46                      injective 2, 130

generalized velocities 45             innovation step 86

general training stage 83             input�output pair 56

genetic algorithms 188                input signals 11

geometric algebra 142                 intellect 192

geometric object 7                    intellegentia 105

Giti 108                              intelligence 105, 198

global 95                             intelligence quotient 147

global factors. 136                   intelligent training control 97

Golgi cells 41, 100                   intelligible world 108

Golgi tendon organs 39                interactionism 199

granule cells 98                      internal local field 94

group 26                              interpolation 85

grows linearly 69                     interpretation 227

                                      introspection 113, 146

Hamilton's canonical equations 46     introvert 212

Hamilton's principle of least action  intuition 142, 211

                                      intuitionistic logic 207

       45                             invariant distribution of states 52

Hamiltonian dynamical system 48       inverse 45

Hamiltonian function 46               inverse�selection 267

Hamiltonian training equations 61     Inverse�selection task 1

Hamiltonian vector field 8            inverse problem 95

Hamming distance 95                   irregular and unpredictable 69

heat bath 52                          irreversible processes 34

heat equation 33                      Ising Hamiltonian 94

heuristic IF�THEN rules 219           Ising spins 93

Hindu scriptures 143                  isometric steady�state contraction 32

holists 143

holonomic brain model 196             jnana 143

homeomorphic immersion 25             joint dissipation 52

homeostatic balance 213               Jungian psychology 209

homomorphism of vector spaces 155

Hotelling's law 156

Hotelling's lemma 156

Index                                323



Karhunen�Lo`eve transform 156        manifest variables 151

Karhunen�Loeve matrix 96             map 2

karma 143                            mapping 2, 65

kernel 2, 3                          map sink 66

kinetic 45                           Markov chain 51

knowledge base 217                   Markov process 51

                                     mass communication 122

L'Hasard et L'Necesite 84            mathematical model 9

lack of memory 51                    maximum likelihood estimator 151

Lagrangian function 45               mean 111, 151

La Logique de Vivant 84              measu�re for the degree of disorder

lamp  laser 72

Langevin 52                                 71

language 105                         memoization 65

latency relaxation 33                memory 192

latent pattern approach 96           mental abilities 105

lateral cisternae 30                 Metaphysics 141

lateral thinking 133                 method of least squares 111

law of conservation of energy 47     methods 1

law of contradiction 207             mezoscopic synergetics 71

law of the excluded middle 207       microscopic hierarchical level of

learning 1, 106

learning dynamics 96                        organization 71

libido 213                           microscopic theory of muscular

Lie algebras 49

Lie groups 26                               contraction 32

limit cycle 66                       middle cerebellar peduncle 42, 100

linear 95, 149                       mind 192

linear map 155                       mind�body problem 197

linear operator 155                  mind maps 143

linear transformation 155            Minu 108

linguistics 123, 125                 model fit 160

logicism 205                         monism 203

logic of life 7                      monitoring 227

long�term memory 262                 Monte�Carlo 150

lookup table 65                      morphism 155

low�pass filter 84                   mossy fibers 42, 101

Lyapunov dimension 77                most efficient technique 271

Lyapunov exponents 66, 77            motor program 83

Lyapunov function 94                 motor servo 14, 39

                                     multi�agent systems 215

MAC address 64                       multiple�intelligence theories 172

macroscopic center�of�mass level 75  multivariate correlation statistical

macroscopic muscle�load dynamics

                                            method 149

       33                            muscle fibers 30

macroscopic system modelling 73      muscular active-state element equation

magnetization 73

maintenance heat 33                         35

manifest pattern approach 96         muscular actuators 52

                                     mutual overlap 95, 96

                                     Myers�Briggs Type Indicator 210

                                     myofibrils 30

                                     myosin 31

324                                    Index



necessary and sufficient condition 2   personality tests 172

necessary condition for existence of   phase�portrait 7

                                       phase�space 7

       chaos 70                        phase�transition theory 70

neural adaptation 118                  phase orbit 49

neurobiology 209                       phase trajectory 49

neurology of creativity 133            phase transition 72

neuroticism 136                        phenomenology 207

new feature 72                         physical 55

non�periodic orbit 169                 Piaget theory 175

nonlinear 95                           plan 105

nonlinearities 55                      planning 227

nonrelativistic quantum mechanics      point orbit 169

                                       political philosophy 194

       167                             Postsynaptic potential 94

nonrigid 165                           potential 45

normal distribution 150                pragmatics 123

normally distributed random variables  Prakrti 198

                                       prediction 5

       151                             prediction/forecasting 227

                                       predictive validity 173

object�oriented programming 216        primary factors 135

object relations theory 214            principal axis factoring 158

oblique factor model 165               principal components analysis 155,

observation 146

obtained 76                                   156

on the macroscopic level 72            principal factor analysis 158

optimism 202                           principal factors 164

order on the microscopic level 72      principal intelligence factor 149

order parameter equations 74           principle of causality 5

order parameter equations of macro-    principle of superposition 55

                                       probability 110

       scopic synergetics 71           probability density function 151

order parameters 70, 95                problem solving 112

organizational communication 123       product�moment 149

original set 2                         production�rule agents 217

output signals 11                      production systems 63

overlap 95                             Promax rotation rotation 162

overloading principle 59               proprioceptive feedback 98

                                       psyche 209

parabolic length�tension curve 32      psychic energy 213

paradigm shift 114                     psychoanalysis 211

parsimony principle 165                psychological tests 172

pattern 66                             psychology 105

patterns 94                            psychometric function 183

peduncles 42, 100                      psychometrics 145

pennate 30                             psychometric testing 145

perception 192                         psychophysics 179

perceptual world 108                   psychoticism 136

perimysium 30                          punishment 121

periodic orbit 169

personality 106, 134

personality psychology 212

Index                                                                                  325



Purkinje cells 98                     sequential (threshold) dynamics 94

Purusha 198                           shadow 210

                                      short�term memory 261

qualitative dynamics 7                shortening heat 33

quantum tunneling 213                 signal detection theory 184

quaternions 142                       simulated annealing 188

                                      sine�integral 84

random walk 51                        singular value decomposition 157

Raven's Progressive Matrices 148      situation 221

Rayleigh � Van der Pol's dissipation  situation awareness 222

                                      six�parameter Euclidean group of

       function 34

reason 105                                   motions 25

reasoning ability 148                 skeletal muscle control system 13

recalls 94                            slaving principle 74

reciprocal activation 39              sliding filament mechanism 32

reciprocal inhibition 39              smooth manifold 8

recognition 1                         sociolinguistics 123

recognize�act cycle 227               space of input signals 55

red and white muscle fibers 30        space of output signals 55

reduce 162                            space rate of change 46

reduces the dimensionally 52          spatio�temporal pattern 66

reflection 143                        specific�situation training stage 83

reinforcement 121                     spectral theorem 157

reinforcement learning 188            speed of convergence 86

representative point 49               spin configurations 94

rotational Hill's parameters 36       spindle receptors 39

Russell Paradox 204                   split�brain 172

                                      spontaneous self-organization and

saddle points 78

sample 151                                   cooperation 70

Sankhya school 198                    sport�training flow 61

sarcolemma 30                         stability 7, 9, 61

sarcomere 31                          stable 61, 78

sarcoplasm 30                         standard deviation 151

sarcoplasmic reticulum 30             standard normal distribution 151

Scholastic tradition 202              standard problem�solving techniques

scientific method 188

scientific revolution 114                    187

score 162                             Stanford�Binet 148

search for truth 200                  state 55, 222

Self 211, 214                         state of an abstract object 56

semantic theory of truth 200          state space 55

semiotics 123                         state variable 56

sensation 211, 221                    statistical�factor 1

sensitivity to initial conditions 70  steady�state movement error 76

sensitivity to parameters 70          steady state 61

sensory adaptation 118                stochastic forces 51

sensory analysis 184                  stochastic influence 52

sensory memory 261                    Storage 262

sensory threshold 183                 stored 94

                                      strange attractor 66

326                                      Index



stretch�reflex 271                       transmission cascade 15

structural equation modelling 159        triad 30

structural stability 8                   Triarchic theory of intelligence 145

sub�net configuration 64                 true beliefs 116

substantial view 193                     truth�in�itself 208

subsumption architecture 219             truth as correspondence 200

superior cerebellar peduncle 42, 101     T tubules 30

supra�personal archetypes 210

surjective 2, 130                        uncertainty 226

syllogism 110                            unconscious complex 210

symmetric coupling 94                    understand 70

symplectic manifold 8                    uniaxial joint 27

symplectic structure 8                   unilocally 6

synaptic efficacy 94                     unique goal 1

synchronicity 210                        uniqueness 2

synergetics 70                           unstable 61

                                         unstable W U manifolds 78

talent model 1, 3, 267                   unstable fixed points 78

talents 1, 267

Tao 203                                  Varimax rotation 161

the angle between the two vectors        vector�field 7

                                         velocity equation 47

       153                               very�large�scale integration 213

theory of cognitive development 175      via 23

thermal equilibrium 70                   virtual 53

thermodynamic relation 33

thermoelastic heat 34                    wave�particle duality 213

the same factor structure 1, 3, 267      weakly�connected neural network

thinking 211

thought 192                                     197

three�point iterative dynamics equation  Weber�Fechner law 180

                                         Wechsler�Bellevue I 149

       170                               Wechsler Adult Intelligence Scale 148

time factor 11                           will 192

top�down object�based goal�oriented      wisdom 106, 141

                                         working memory 261

       approach 174                      wrapper 156

torque-time 35

trans�derivational search 66             yang 213

transformation rules 208                 Yerkes�Dodson Law 139

transient 61                             yin 213

translational and rotational Lie groups



       49

Cognitive Systems Monographs



Edited by R. Dillmann, Y. Nakamura, S. Schaal and D. Vernon



Vol. 1: Arena, P.; Patan�, L. (Eds.)

Spatial Temporal Patterns for

Action-Oriented Perception

in Roving Robots

425 p. 2009 [978-3-540-88463-7]



Vol. 2: Ivancevic, T.T.; Jovanovic, B.;

Djukic, S.; Djukic, M.; Markovic, S.

Complex Sports Biodynamics

326 p. 2009 [978-3-540-89970-9]