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CLASSICAL MECHANICS
SOLUTIONS MANUAL
R. Douglas Gregory
November 2006
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2
Contents
1 The algebra and calculus of vectors 2 Velocity, acceleration and scalar angular velocity 3 Newton¡¯s laws of motion and the law of gravitation 4 Problems in particle dynamics 5 Linear oscillations and normal modes 6 Energy conservation 7 Orbits in a central ?eld 8 Non-linear oscillations and phase space 9 The energy principle 10 The linear momentum principle 11 The angular momentum principle 12 Lagrange¡¯s equations and conservation principles 13 The calculus of variations and Hamilton¡¯s principle 14 Hamilton¡¯s equations and phase space 15 The general theory of small oscillations 16 Vector angular velocity 17 Rotating reference frames 18 Tensor algebra and the inertia tensor 19 Problems in rigid body dynamics 3 27 62 76 139 179 221 276 306 335 381 429 473 505 533 577 590 615 646
Chapter One T¡¦(»ý·«)