Classical Mechanics With Applications

by Johnson, Porter Wear

• ISBN13: 9789814304153
• ISBN10: 9814304158
• Format: Hardcover
• Copyright: 2010-02-24
• Publisher: World Scientific Pub Co Inc

Summary

This textbook appropriate for a one-semester course in classical mechanics at the late undergraduate or early graduate level presents a fresh, modern approach to mechanics. About 150 exercises, covering a wide variety of topics and applications, have solutions roughly outlined for enhanced understanding. Unique to this text is the versatile application of programming language Mathematica[[ throughout to analyze systems and generate results. Coverage is also devoted to the topic on one dimensional continuum systems. The extensive discussions on inverse problems of mechanical systems and the detailed analysis of stability of classical systems certainly make this an outstanding textbook.

Table of Contents

Preface	p. v
Introduction	p. 1
Calculus of Variations	p. 1
Geodesics on a Sphere	p. 2
Lagrangian Mechanics	p. 4
Equivalence of Euler-Lagrange Equations to Newton's Second Law	p. 6
Catenary	p. 8
Brachistochrone	p. 11
Exercises	p. 13
One Degree of Freedom	p. 23
Harmonic Oscillator; Damping	p. 23
Another Example of One Dimensional Motion	p. 25
Falling Object; Terminal Speed	p. 27
Huygens' Pendulum	p. 28
Plane Pendulum	p. 30
Quartic (Duffing) Oscillator	p. 33
van der Pol Equation	p. 35
Inverse Problem	p. 37
Linear Rocket Motion	p. 39
Exercises	p. 40
Systems with a Few Degrees of Freedom	p. 53
Projectiles; Air Resistance	p. 53
Spherical Pendulum	p. 54
Two-dimensional Harmonic Motion	p. 58
Planar Double Pendulum	p. 61
Triple Pendulum	p. 63
Central Forces	p. 64
Holonomic and Non-holonomic Constraints	p. 66
Exercises	p. 68
Systems of Particles	p. 79
Lagrangian for Several Particles; Noether's Theorem	p. 79
Center of Mass	p. 81
Rigid Bodies: Moment of Inertia	p. 84
Euler Angles	p. 88
Axially Symmetric Top	p. 90
Euler Equations	p. 91
Rotation about an Axis	p. 93
Exercises	p. 96
Noninertial Coordinate Systems	p. 107
Accelerated Reference Frame	p. 107
Rotating Frame	p. 108
Bodies Falling to the Ground	p. 110
Projectile Motion	p. 111
Foucault Pendulum	p. 113
Exercises	p. 114
Gravitation	p. 127
Kepler's Laws	p. 127
Inverse Square Force	p. 128
Two Body Problem	p. 132
Restricted Three Body Problem	p. 133
Stability of L4 and L5	p. 136
Gravity from a Mass Distribution	p. 137
Deviations from Newtonian Gravitation: Precession	p. 138
The Tides	p. 140
Exercises	p. 141
Collisions and Scattering	p. 155
Collinear, Elastic Collisions	p. 155
Classical Zeno Process	p. 157
Non-collinear Elastic Collisions	p. 159
Scattering from Hard Sphere	p. 161
Scattering by Central Potential	p. 162
Rutherford Scattering	p. 164
Cross Section for Repulsive 1/r4 Potential	p. 165
Inverse Scattering Problem	p. 169
Exercises	p. 173
Hamiltonian Mechanics	p. 183
Hamilton's Equations	p. 183
Poisson Brackets	p. 185
Canonical Transformations	p. 187
Hamilton Jacobi Equation	p. 190
Maupertuis Principle	p. 196
Adiabatic Invariance of Action	p. 197
Exercises	p. 198
Stability and Instability	p. 213
Driven Inverted Pendulum	p. 213
Harmonically Driven Inverted Pendulum	p. 219
Driven Pendulum	p. 222
Parametric Resonance	p. 225
Driven Harmonic Oscillator	p. 226
Driven Duffing Oscillator	p. 230
Hénon-Heiles Model; KAM Theorem	p. 232
Exercises	p. 234
Continuous Systems	p. 253
Symmetric Ring	p. 253
Masses on String: Continuous Limit	p. 255
Finite String	p. 258
Non-uniform String	p. 260
Exercises	p. 261
Appendix Supplementary Topics	p. 271
Special Functions	p. 271
Some Principal Figures in Mechanics	p. 274
Bibliography	p. 275
Index	p. 277
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