[图书简介]

This comprehensive volume is a graduate-level text in human biodynamics, written in the unified categorical language of modern differential geometry and topology. Combining mathematics, physics and robotics with human physiology, this is the first book that describes all levels of human biodynamics, from musculo-skeletal mechanics to the higher brain functions. The book develops and uses a variety of research methods, ranging from chaos theory and Haken's synergetics, through quantum mechanics, to nonlinear control and artificial intelligence, to provide the means to understand, predict and control the behavior of human-like systems in their full neuro-musculo-skeletal complexity. The applications of this unique scientific methodology range from prediction of human neuro-musculo-skeletal injuries to brain-like control of humanoid robots.
[Table Of Contents]

Preface

Glossary of Frequently Used Symbols

1. Introduction

1.1 The Problem of Natural Biodynamics

1.2 A Brief History of Biodynamics

1.3 Mechanical Basis of Biodynamics

1.4 Conservative versus Dissipative Hamiltonian Dynamics

1.5 Neural Basis of Biodynamics

2. Natural Language of Biodynamics

2.1 Categorical Metalanguage

2.2 The Basics of Dynamics

2.3 Chaos and Synergetics in Biodynamics

3. Natural Geometry of Biodynamics

3.1 Motivation for Geometry in Biodynamics

3.2 Biodynamic Manifold M

3.3 Biodynamic Bundles

3.4 Sections of Biodynamic Bundles

3.5 Lie Categories in Biodynamics

3.6 Riemannian Geometry in Biodynamics

3.7 Symplectic Geometry in Biodynamics

3.8 Impulse Biodynamics and Synthetic Geometry

3.9 A Quick Look at Modern Geometrodynamics

3.10 3D Modelling and Animation in Biodynamics

3.11 Kinematics of Biomechanical Chains

4. Natural Mechanics of Biodynamics

4.1 Lagrangian Formalism in Biodynamics

4.2 Hamiltonian Formalism in Biodynamics

4.3 Quantum Formalism in Nano-Biodynamics

4.4 Variational Formalism in Biodynamics

4.5 Nonholonomic Biodynamics

4.6 Stochastic Formalism in Biodynamics

4.7 Muscular Excitation-Contraction Dynamics

4.8 Lie Functors in Biodynamics

4.9 Mechanics of Spinal Injuries

5. Natural Topology of Biodynamics

5.1 Category of (Co)Chain Complexes in Biodynamics

5.2 Natural Duality in Biodynamics

5.3 Topological Phase Transitions and Hamiltonian Chaos

5.4 The Covariant Force Functor

6. Natural Control and Self-Organization in Biodynamics

6.1 The Basics of Classical Control and Stability

6.2 The Basis of Modern Geometric Control

6.3 Modern Control Techniques for Mechanical Systems

6.4 Locomotion Systems and Human Gait

6.5 Biodynamic Control Policy, Learning and Self-Organization

6.6 Essentials of Biodynamic Measurement: Kalman Filtering and Inertial Navigation

6.7 Humanoid Robotics

7. Natural Brain Dynamics and Sensory?otor Integration

7.1 Introduction to Brain

7.2 Human Nervous System

7.3 The Sensory-Motor Adjunction

7.4 Brain Dynamics

7.5 Biological Neural Nets

7.6 Artificial Neural Nets in Biodynamics

7.7 Distinguished ANN Models

7.8 Fuzzy Logic in Biodynamics

7.9 Natural System in a Category

7.10 Brain?ind Functorial Machines

7.11 Body?ind Adjunction and Natural Psychodynamics

7.12 Brain?ike Control in a Nutshell

Appendix A

A.1 Basic Formulas from Tensor Analysis

A.2 Frequently Used Neurophysiological Terms

A.3 Modern 3D Neuroimaging

A.4 Complex Functions, Manifolds and Hilbert Spaces

A.5 Classical Lie Theory

A.6 Phase Transitions, Partition Function and Noise

A.7 MathematicaTm Derivation of Main Biodynamic Functions

Bibliography

Index