🎾 Complex Sports Biodynamics With Practical Applications In Tennis¶
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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
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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]