Nonholonomic Mechanics and Control
Nonholonomic Mechanics and Control develops the rich connections between control theory and geometric mechanics. Control theory is linked with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations and especially with the theory of nonholonomic mechanics (mechanical systems subject to motion constraints). Both controllability and optimal control are treated, including the Pontryagin maximum principle. In addition, the stability, control, and stabilization of mechanical systems are discussed. In particular, these items are considered for nonholonomic systems. The aim of the book is to provide a unified treatment of nonlinear control theory and constrained mechanical systems, incorporating material that has not yet made its way into texts and monographs. Detailed illustrations and exercises are included throughout the text.
This book is intended for graduate and advance undergraduate students in mathematics, physics and engineering who wish to learn this subject and for researchers in the area who want to enhance their techniques.
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Foundations of Mechanics: A Mathematical Exposition of Classical Mechanics ...
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and NewtonEuler Balance
12 Hamiltons Principle
13 The LagrangedAlembert Principle
14 The Vertical Rolling Disk
15 The Falling Rolling Disk
16 The Knife Edge
17 The Chaplygin Sleigh
44 Averaging and Trajectory Planning
46 Hamiltonian and Lagrangian Control Systems
51 Equations of Motion
52 The LagrangedAlembert Principle
53 Projected Connections and Newtons Law
54 Systems with Symmetry
18 The Heisenberg System
19 The Rigid Body
110 The Roller Racer
111 The Rattleback
112 The Toda Lattice
22 Differentiable Manifolds
24 Center Manifolds
25 Differential Forms
26 Lie Derivatives
27 Stokess Theorem Riemannian Manifolds Distributions
28 Lie Groups
29 Fiber Bundles and Connections
Basic Concepts in Geometric Mechanics
31 Symplectic and Poisson Manifolds and Hamiltonian Flows
32 Cotangent Bundles
33 Lagrangian Mechanics and Variational Principles
34 Mechanical Systems with External Forces
35 LiePoisson Brackets and the Rigid Body
36 The EulerPoincare Equations
37 Momentum Maps
38 Symplectic and Poisson Reduction
39 A Particle in a Magnetic Field
310 The Mechanical Connection
311 The LagrangePoincaré Equations
312 The EnergyMomentum Method
313 Coupled Planar Rigid Bodies
314 Phases and Holonomy the Planar Skater
An Introduction to Aspects of Geometric Control Theory
42 Controllability and Accessibility
43 Representation of System Trajectories
55 The Momentum Equation
56 Examples of the Nonholonomic Momentum Map
57 More General Nonholonomic Systems with Symmetries
58 The Poisson Geometry of Nonholonomic Systems
Control of Mechanical and Nonholonomic Systems
62 Stabilization of the Heisenberg System
63 Stabilization of a Generalized Heisenberg System
64 Controllability Accessibility and Stabilizability
65 Smooth Stabilization to a Manifold
66 Nonsmooth Stabilization
67 Nonholonomic Systems on Riemannian Manifolds
72 Optimal Control and the Maximum Principle
73 Variational Nonholonomic Systems and Optimal Control
74 Kinematic SubRiemannian Optimal Control Problems
75 Optimal Control and a Particle in a Magnetic Field
76 Optimal Control of Mechanical Systems
Stability of Nonholonomic Systems
83 The Pure Transport Case
84 The Nonpure Transport Case
85 General Case the LyapunovMalkin Method
86 EulerPoincaréSuslov Equations
EnergyBased Methods for Stabilization of Controlled Lagrangian Systems
92 Feedback Design and Matching
93 Stabilization of a Class of Nonholonomic Systems
94 Averaging for Controlled Lagrangian Systems
95 Dynamic Nonholonomic Averaging
Additional Bibliography: Nonholonomic Mechanics and Control References
REFERENCES. 1. Additional Bibliography: Nonholonomic Mechanics and. Control. 1st Edition, 1st Printing. Version: May 5, 2004. Anthony Bloch, ...
www.cds.caltech.edu/ mechanics_and_control/ errata/ 2004-05-05/ Bloch_biblio_2004-05-05.pdf
Holonomic and Nonholonomic Constraints
Nonholonomic Mechanics and Control. links control theory with a geometric. view of classical mechanics in both its. Lagrangian and Hamiltonian formula- ...
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