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CLASSICAL MECHANICS
SOLUTIONS MANUAL
R. Douglas Gregory
November 2006
³»¿ë¹°ÀÔ´Ï´Ù.
Contents

1 The algebra and calculus of vectors 3

2 Velocity, acceleration and scalar angular velocity 27

3 Newtons laws of motion and the law of gravitation 62

4 Problems in particle dynamics 76

5 Linear oscillations and normal modes 139

6 Energy conservation 179

7 Orbits in a central field 221

8 Non-linear oscillations and phase space 276

9 The energy principle 306

10 The linear momentum principle 335

11 The angular momentum principle 381

12 Lagranges equations and conservation principles 429

13 The calculus of variations and Hamiltons principle 473

14 Hamiltons equations and phase space 505

15 The general theory of small oscillations 533

16 Vector angular velocity 577

17 Rotating reference frames 590

18 Tensor algebra and the inertia tensor 615

19 Problems in rigid body dynamics 646

º»¹®/³»¿ë
CLASSICAL MECHANICS

SOLUTIONS MANUAL

R. Douglas Gregory

November 2006

Please report any errors in these solutions by emailing

cm : solutions@btinternet :com

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·«)



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