Human-Like Biomechanics

by Ivancevic, Vladimir G.; Ivancevic, Tijana T.

• ISBN13: 9781402041167
• ISBN10: 1402041160
• Format: Hardcover
• Copyright: 2006-03-30
• Publisher: Springer Verlag

Summary

Human-Like Biomechanics is a comprehensive introduction into modern geometrical methods to be used as a unified research approach in two apparently separate and rapidly growing fields: mathematical biomechanics and humanoid robotics. The term human-like biomechanics is used to denote this unified modelling and control approach to humanoid robotics and mathematical biomechanics, based on theoretical mechanics, differential geometry and topology, nonlinear dynamics and control, and path-integral methods. From this geometry-mechanics-control modelling perspective, "human" and "humanoid" means the same. This unified approach enables both design of humanoid systems of immense complexity and prediction/prevention of subtle neuro-musculo-skeletal injuries. This approach has been realized in the form of the world-leading human-motion simulator with 264 powered degrees of freedom, called Human Biodynamics Engine (developed in Defence Science & Technology Organisation, Australia). The book contains six Chapters and an Appendix. The first Chapter is an Introduction, giving a brief review of mathematical techniques to be used in the text. The second Chapter develops geometrical basis of human-like biomechanics, while the third Chapter develops its mechanical basis, mainly from generalized Lagrangian and Hamiltonian perspective. The fourth Chapter develops topology of human-like biomechanics, while the fifth Chapter reviews related nonlinear control techniques. The sixth Chapter develops covariant biophysics of electro-muscular stimulation. The Appendix consists of two parts: classical muscular mechanics and modern path integral methods, which are both used frequently in the main text. The whole book is based on the authors' own research papers in human-like biomechanics.

Table of Contents

Preface	xi
Acknowledgments	xiv
Glossary of Frequently Used Symbols	1	(4)
Introduction	5	(58)
Local Tensorial Language of Human--Like Biomechanics	6	(24)
Classical Translational Biomechanics	6	(2)
Calculus of Geometric Objects	8	(10)
Lagrangian Action and Feynman Path Integral	18	(4)
Noether Theorem	22	(2)
Symplectic Mechanics	24	(1)
Modern Rotational Biomechanics	25	(3)
Muscular Dynamics and Control	28	(2)
Global Functorial Language of Human--Like Biomechanics	30	(33)
Preliminaries from Calculus, Algebra and Topology	31	(11)
Categories	42	(4)
Functors	46	(2)
Natural Transformations	48	(3)
Limits and Colimits	51	(1)
The Adjunction	52	(1)
n--Categories	53	(7)
Abelian Functorial Algebra	60	(3)
Geometric Basis of Human--Like Biomechanics	63	(128)
Biomechanical Manifold M	63	(3)
Definition of the Manifold M	64	(1)
Smooth Maps Between Manifolds	65	(1)
Biomechanical Bundles	66	(13)
The Tangent Bundle of the Manifold M	66	(2)
The Cotangent Bundle of the Manifold M	68	(1)
Fibre Bundles	69	(8)
Jet Bundles	77	(2)
Sections of Biomechanical Bundles	79	(23)
Biomechanical Evolution and Flow	79	(1)
Vector--Fields and Their Flows	80	(7)
Differential Forms on M	87	(15)
Lie Categories in Human--Like Biomechanics	102	(54)
Lie Derivative in Biomechanics	102	(8)
Lie Groups in Human--Like Biomechanics	110	(16)
Dynamical Games on Lie Groups	126	(8)
Group Structure of the Biomechanical Manifold M	134	(4)
Lie Symmetries in Biomechanics	138	(18)
Riemannian Geometry in Human--Like Biomechanics	156	(28)
Local Riemannian Geometry on M	157	(8)
Global Riemannian Geometry on M	165	(11)
Complex and Kahler Manifolds	176	(5)
Conformal Killing--Riemannian Geometry	181	(3)
Symplectic Geometry in Human--Like Biomechanics	184	(4)
Symplectic Algebra	185	(1)
Symplectic Geometry on M	185	(2)
Momentum Map and Symplectic Reduction of M	187	(1)
The Covariant Force Functor	188	(3)
Mechanical Basis of Human--Like Biomechanics	191	(98)
Lagrangian Formalism in Human--Like Biomechanics	191	(5)
Basis of Lagrangian Mechanics	193	(2)
Basics of Poincare Dynamics	195	(1)
Hamiltonian Formalism in Human--Like Biomechanics	196	(38)
Nonlinear Dynamics in Hamiltonian Form	198	(19)
Hamiltonian Geometry in Human--Like Biomechanics	217	(2)
Hamilton--Poisson Geometry in Biomechanics	219	(5)
Completely Integrable Hamiltonian Systems	224	(7)
Killing Vector and Tensor Fields in Biomechanics	231	(3)
Variational Formalism in Human--Like Biomechanics	234	(17)
Biomechanical Action Functional	235	(1)
Lagrangian Action	235	(2)
Hamiltonian Action	237	(1)
Hamiltonian--Action Formulation of Biomechanics	238	(2)
Maupertuis Stationary Action in Biomechanics	240	(2)
Geometric Action	242	(5)
Feynman Quantum--Mechanical Action	247	(4)
Nonholonomic Problems in Human--Like Biomechanics	251	(21)
Lagrangian Approach	251	(2)
Hamiltonian Approach	253	(1)
Biomechanical Example: Bicycle Dynamics	254	(2)
Constraint Dirac--Hamiltonian Dynamics	256	(16)
Lie Functors in Human--Like Biomechanics	272	(14)
Lie-Lagrangian Biomechanical Functor	272	(6)
Lie--Hamiltonian Biomechanical Functor	278	(4)
Stochastic--Lie--Hamiltonian Biomechanical Functor	282	(1)
Fuzzy--Stochastic--Lie--Hamiltonian Functor	283	(3)
Biomechanics of Spinal Injuries	286	(3)
Topology of Human--Like Biomechanics	289	(24)
Category of (Co)Chain Complexes in Human--Like Biomechanics	289	(3)
(Co)Homologies in Abelian Categories Related to M	290	(1)
M--Reduction and its Euler Characteristic	291	(1)
Morse Theory in Human--Like Biomechanics	292	(9)
Morse Geometry of M	292	(5)
Morse Topology of M	297	(4)
Hodge--De Rham Theory in Human--Like Biomechanics	301	(3)
Hodge Laplacian on M	301	(2)
Heat Kernel and Thermodynamics on M	303	(1)
Topological Duality in Human--Like Biomechanics	304	(9)
Geometric Duality Theorem for M	305	(4)
Topological Duality Theorem for M	309	(2)
Lagrangian Versus Hamiltonian Duality	311	(1)
Globally Dual Structure of Rotational Biomechanics	312	(1)
Nonlinear Control in Human--Like Biomechanics	313	(58)
The Basics of Classical Control and Stability	313	(12)
Brief Introduction into Feedback Control	313	(5)
Linear Stationary Systems and Operators	318	(4)
Stability and Boundedness	322	(2)
Lyapunov's Stability Method	324	(1)
The Basis of Modern Geometric Control	325	(13)
Feedback Linearization	325	(8)
Controllability	333	(5)
Modern Control Techniques for Mechanical Systems	338	(14)
Abstract Control System	338	(1)
Controllability of a Linear Control System	339	(1)
Affine Control System and Local Controllability	340	(1)
Lagrangian Control Systems	340	(8)
Lie--Adaptive Control in Human--Like Biomechanics	348	(2)
Intelligent Robot Control: Interaction with Environment	350	(2)
Neural Path Integral Motion Controller	352	(5)
Spinal Autogenetic Reflex Control	353	(1)
Cerebellum -- the Comparator	354	(2)
Hamiltonian Action and Neural Path Integral	356	(1)
Brain--Like Control Functor in Human--Like Biomechanics	357	(14)
Covariant Biophysics of Electro--Muscular Stimulation	371	(20)
Basics of Electrical Muscular Stimulation	371	(4)
EMS Functor	375	(4)
Global macro--level of EMStotal	375	(2)
Local Micro--Level of EMStotal	377	(1)
Micro--Level Adaptation and Muscular Training	378	(1)
Electrical Stimulation Fields: EMSfields	379	(3)
External Smooth Maxwell Electrodynamics	379	(2)
Internal Cellular Bio--Quantum Electrodynamics	381	(1)
Stimulated Muscular Contraction Paths: EMSpaths	382	(2)
External Anatomical Muscular Mechanics	382	(1)
Internal Myofibrillar Bio--Quantum Mechanics	382	(2)
Anatomical Geometry of the Face & Body Shape: EMSgeom	384	(7)
External Face & Body Geometry	384	(5)
Cellular Muscle--Fat Geometry	389	(2)
A Appendix	391	(48)
A.1 Basic Formulas from Tensor Analysis	391	(17)
A.1.1 Transformation of Coordinates and Elementary Tensors	391	(6)
A.1.2 Euclidean Tensors	397	(1)
A.1.3 Tensor Derivatives on Riemannian Manifolds	398	(7)
A.1.4 The Covariant Force Law in Human--Like Biomechanics	405	(2)
A.1.5 The Essence of Hamiltonian Biomechanics	407	(1)
A.2 Muscular System	408	(11)
A.2.1 Muscular Histology	408	(2)
A.2.2 Classical Theories of Muscular Contraction	410	(7)
A.2.3 The Equivalent Muscular Actuator	417	(1)
A.2.4 Biochemistry of Muscular Contraction	418	(1)
A.3 Path Integral Methods	419	(20)
A.3.1 Historical Remarks	419	(8)
A.3.2 Standard Path Integral Quantization	427	(8)
A.3.3 Modern String Actions and Transition Amplitudes	435	(4)
References	439	(16)
Index	455