A stimulating, modern approach to analytical mechanics Analytical Mechanics with an Introduction to Dynamical Systems offers a much-needed, up-to-date treatment of analytical dynamics to meet the needs of today's students and professionals. This outstanding resource offers clear and thorough coverage of mechanics and dynamical systems, with an approach that offers a balance between physical fundamentals and mathematical concepts. Exceptionally well written and abundantly illustrated, the book contains over 550 new problems-more than in any other book on the subject-along with user-friendly computational models using MATLAB. Featured topics include: * An overview of fundamental dynamics, both two- and three-dimensional * An examination of variational approaches, including Lagrangian theory * A complete discussion of the dynamics of rotating bodies * Coverage of the three-dimensional dynamics of rigid bodies * A detailed treatment of Hamiltonian systems and stability theory Ideal for advanced undergraduate and graduate students in mechanical engineering, physics, or applied mathematics, this distinguished text is also an excellent self-study or reference text for the practicing engineer or scientist.

<b>JOSEF S. T+R+K</b> is a professor in the Department of Mechanical Engineering at the Rochester Institute of Technology in Rochester, New York.

Preface

xi

Acknowledgments

xiii

Principles Of Dynamics

1

(87)

Mechanics

2

(1)

Basic Principles of Mechanics

3

(2)

Kinematics

5

(5)

Coordinate Transformations

10

(1)

Time Rate of Change of a Unit Vector

11

(3)

Kinetics

14

(3)

Work and Energy

17

(4)

Conservative Systems

21

(8)

Systems of Particles

29

(7)

Motion in Noninertial Reference Frames

36

(5)

Planar Motion of Rigid Bodies

41

(2)

Virtual Work

43

(3)

Problems

46

(42)

Lagrangian Dynamics

88

(71)

Generalized Coordinates

89

(5)

Constraints

94

(3)

Holonomic Systems

97

(2)

Kinetic Energy and Generalized Momenta

99

(3)

Generalized Force

102

(5)

Lagrange's Equations of Motion

107

(5)

Conservative Systems

112

(1)

Lagrangian Systems

113

(2)

Dissipative Systems

115

(2)

Forces of Constraint

117

(4)

Integrals of Motion

121

(4)

Ignorable Coordinates

125

(3)

Steady Motion

128

(3)

Lagrange's Equations for Impulsive Forces

131

(2)

Electromechanical Analogies

133

(2)

Problems

135

(24)

Calculus Of Variations

159

(34)

Introduction

159

(5)

Extrema of Functions

164

(1)

Necessary Conditions for an Extremum

165

(4)

Special Cases of the Euler-Lagrange Equation

169

(2)

The Variational Operator

171

(1)

Natural Boundary Conditions

172

(2)

Generalizations

174

(1)

Several Independent Variables

175

(1)

Variational Problems with Constraints

176

(3)

Hamilton's Principle

179

(6)

Problems

185

(8)

Dynamics Of Rotating Bodies

193

(55)

Kinematics of Rotating Bodies

193

(4)

Motion Relative to Moving Axes

197

(2)

Rigid-Body Dynamics

199

(3)

The Inertia Tensor

202

(3)

Translation Theorem for Angular Momentum

205

(1)

Kinetic Energy

206

(1)

Equations of Motion for a Rigid Body

207

(1)

Euler's Equations of Motion for a Rotating Body

208

(1)

Moment-Free Motion

209

(5)

General Case

214

(2)

Euler Angles

216

(4)

Gyrodynamics

220

(3)

Steady Precession

223

(1)

General Solution

224

(4)

Problems

228

(20)

Hamiltonian Systems

248

(40)

Introduction

248

(1)

Legendre Transformations

249

(2)

Hamilton's Canonical Equations

251

(2)

The Hamiltonian Function

253

(2)

Ignorable Coordinates

255

(2)

Phase Space

257

(2)

Hydrodynamical Analogy

259

(4)

Canonical Transformations

263

(5)

Generating Functions

268

(1)

Examples of Generating Functions

269

(3)

Hamilton-Jacobi Equation

272

(2)

Conservative Systems

274

(1)

Separation of Variables

275

(3)

Problems

278

(10)

Stability Theory

288

(41)

Introduction

288

(2)

Definition of Stability

290

(6)

The Variational Equations

296

(4)

Stability of Linear Systems

300

(6)

Higher Order Systems

306

(2)

Lyapunov's Direct Method

308

(7)

Examples

315

(4)

Problems

319

(10)

APPENDIX A VECTOR ANALYSIS

329

(12)

Vectors

329

(2)

Scalar or Dot Product

331

(1)

Vector (Cross) Product

332

(3)

Vector Functions

335

(1)

Differential Operators

336

(2)

Conservative Vector Fields

338

(1)

Integral Theorems

338

(1)

Line Integrals

339

(2)

APPENDIX B SEPARATION OF VARIABLES

341

(4)

APPENDIX C NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

345

(8)

First-Order Differential Equations

345

(4)

Systems of Ordinary Differential Equations

349

(1)

Higher Order Equations

350

(1)

Errors and Stability

351

(2)

Index

353

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Analytical Mechanics With an Introduction to Dynamical Systems

9780471332077

0471332070

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