CLASSICAL MECHANICS SOLUTIONS MANUAL R. Douglas Gregory November 2006 Please report any errors in these solutions by emailing cm :
[email protected] :com 2 Contents 1 The algebra and calculus of vectors 3 2 Velocity, acceleration and scalar angular velocity 27 3 Newton’s 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 Lagrange’s equations and conservation principles 429 13 The calculus of variations and Hamilton’s principle 473 14 Hamilton’s 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 Chapter One The algebra and calculus of vectors c Cambridge University Press, 2006 4 Chapter 1 The algebra and calculus of vectors Problem 1 . 1 In terms of the standard basis set fi ; j ; kg, a D 2 i c D i 5 j C 3 k. j 2k, b D 3 i 4 k and Find 3 a C 2 b 4 c and j a b j2 . Find j a j, j b j and a b. Deduce the angle between a and b. Find the component of c