Nonholonomic Mechanics and Control,9780387955353

Nonholonomic Mechanics and Control

by ; ; ;
ISBN13: 9780387955353
ISBN10: 0387955356
Format: Hardcover
Pub. Date: 2003-07-01
Publisher(s): Springer Verlag
  • Free Shipping Icon

    This Item Qualifies for Free Shipping!*

    *Excludes marketplace orders.

List Price: $84.99

Rent Textbook

Select for Price
Add to Cart
There was a problem. Please try again later.

Rent Digital

Rent Digital Options
Online:30 Days access
Downloadable:30 Days
$30.60
Online:60 Days access
Downloadable:60 Days
$40.80
Online:90 Days access
Downloadable:90 Days
$51.00
Online:120 Days access
Downloadable:120 Days
$61.20
Online:180 Days access
Downloadable:180 Days
$66.30
Online:1825 Days access
Downloadable:Lifetime Access
$101.99
*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.
$66.30*
Add to Cart

New Textbook

We're Sorry
Sold Out

Used Textbook

We're Sorry
Sold Out

Buy from our Marketplace starting at $129.03

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

The goal of this book is to explore some of the connections between control theory and geometric mechanics; that is, control theory is linked with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations and in particular with the theory of mechanical systems subject to motion constraints. The synthesis of topics is appropriate as there is a particularly rich connection between mechanics and nonlinear control theory. The aim is to provide a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material that has not yet made its way into texts and monographs.This book is intended for graduate students who wish to learn this subject and researchers in the area who want to enhance their techniques.

Table of Contents

Preface v
About the Authors xi
A Diagram for the Book xvii
Introduction
1(48)
Generalized Coordinates and Newton--Euler Balance
2(4)
Hamilton's Principle
6(5)
The Lagrange-d'Alembert Principle
11(4)
The Vertical Rolling Disk
15(6)
The Falling Rolling Disk
21(2)
The Knife Edge
23(2)
The Chaplygin Sleigh
25(4)
The Heisenberg System
29(5)
The Rigid Body
34(8)
The Roller Racer
42(1)
The Rattleback
43(2)
The Toda Lattice
45(4)
Mathematical Preliminaries
49(70)
Vector Fields, Flows, and Differential Equations
49(13)
Differentiable Manifolds
62(9)
Stability
71(3)
Center Manifold
74(5)
Differential Forms
79(7)
Lie Derivatives
86(7)
Stokes's Theorem, Riemannian Manifolds, Distributions
93(4)
Lie Groups
97(8)
Fiber Bundles and Connections
105(14)
Basic Concepts in Geometric Mechanics
119(56)
Symplectic and Poisson Manifolds and Hamiltonian Flows
120(3)
Cotangent Bundles
123(1)
Lagrangian Mechanics and Variational Principles
124(4)
Mechanical Systems with External Forces
128(2)
Lie--Poisson Brackets and the Rigid Body
130(4)
The Euler--Poincare Equations
134(2)
Momentum Maps
136(3)
Symplectic and Poisson Reduction
139(3)
A Particle in a Magnetic Field
142(2)
The Mechanical Connection
144(2)
The Lagrange--Poincare Equations
146(4)
The Energy-Momentum Method
150(8)
Coupled Planar Rigid Bodies
158(9)
Phases and Holonomy, the Planar Skater
167(8)
Introduction to Aspects of Geometric Control Theory
175(32)
Nonlinear Control Systems
175(2)
Controllability and Accessibility
177(5)
Representation of System Trajectories
182(8)
Averaging and Trajectory Planning
190(4)
Stabilization
194(4)
Hamiltonian and Lagrangian Control Systems
198(9)
Nonholonomic Mechanics
207(70)
Equations of Motion
211(5)
The Lagrange--d'Alembert Principle
216(5)
Projected Connections and Newton's Law
221(2)
Systems with Symmetry
223(5)
The Momentum Equation
228(10)
Examples of the Nonholonomic Momentum Map
238(10)
More General Nonholonomic Systems with Symmetries
248(6)
Poisson Geometry of Nonholonomic Systems
254(23)
Control of Mechanical and Nonholonomic Systems
277(52)
Background in Kinematic Nonholonomic Control Systems
277(8)
Stabilization of the Heisenberg System
285(6)
Stabilization of a Generalized Heisenberg System
291(10)
Controllability, Accessibility, and Stabilizability
301(3)
Smooth Stabilization to a Manifold
304(4)
Nonsmooth Stabilization
308(11)
Nonholonomic Systems on Riemannian Manifolds
319(10)
Optimal Control
329(38)
Variational Nonholonomic Problems
329(7)
Optimal Control and the Maximum Principle
336(3)
Variational Nonholonomic Systems and Optimal Control
339(3)
Kinematic Sub-Riemannian Optimal Control Problems
342(11)
Optimal Control and a Particle in a Magnetic Field
353(5)
Optimal Control of Mechanical Systems
358(9)
Stability of Nonholonomic Systems
367(32)
The Nonholonomic Energy-Momentum Method
367(3)
Overview
370(2)
The Pure Transport Case
372(5)
The Nonpure Transport Case
377(10)
General Case---the Lyapunov--Malkin Method
387(5)
Euler--Poincare--Suslov Equations
392(7)
Energy-Based Methods for Stabilization
399(40)
Controlled Lagrangian Methods
399(3)
Feedback Design and Matching
402(8)
Stabilization of a Class of Nonholonomic Systems
410(5)
Averaging for Controlled Lagrangian Systems
415(20)
Dynamic Nonholonomic Averaging
435(4)
References 439(32)
Index 471

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.