Theoretical Mechanics-理论力学-英文版

Introduction 1
Chapter 1 Kinematics of Particles 3
1.1 Description of the particle motion 3
1.2 Representation of velocity and acceleration in components 8
Questions 13

Chapter 2 Dynamics of Particles 14
2.1 Basic laws of dynamics 14
2.2 Work and energy 18
2.3 Equation of motion 23
2.4 Velocity瞕ependent equation of motion 29
2.5 Position瞕ependent equation of motion 36
2.6 Inertial and non瞚nertial reference system, Galileo principle of relativity 40
2.7 Fundamental laws and conservation laws 44
Questions 49

Chapter 3 Mechanics of the particle group 51
3.1 Particle group 51
3.2 Theorem of momentum and conservation of momentum 53
3.3 Theorem of angular momentum and conservation of angular
momentum 56
3.4 Theorem of kinetic energy and conservation of energy 59
3.5 Two瞓ody problem 62
3.6 Center of mass coordinate and laboratory coordinate 65
3.7 Motion of the variable mass 69
Questions 74

Chapter 4 Mechanics of rigid body 75
4.1 Description of the rigid body motion 75
4.2 Vector of angular velocity 77
4.3 Euler angles 81
4.4 Motion equation of the rigid body 83
4.5 Principal axes transformation and inertia ellipsoid 86
4.6 Euler’s equation of motion and symmetrical top 92
4.7 Motion in non瞚nertia system 95
4.8 Application of non瞚nertia system 99
Questions 105

Chapter 5 Analytical mechanics 106
5.1 Generalized coordinates and generalized force 106
5.2 Lagrangian equation 111
5.3 Variational principles of mechanics 116
5.4 Symmetry and conservation law 121
5.5 Lagrangian undetermined multiplies 126
5.6 Hamiltonian equations of motion 130
5.7 Canonical transformation, Hamilton睯acobi equation 135
5.8 Poisson bracket, phase space and Liouville’s theorem 140

Questions 143

Chapter 6 Central Force 145
6.1 Motion in central force field 145
6.2 Effective potential and general solutions 149
6.3 Inverse square law of force 153
6.4 Stability of orbits and perturbation 158
6.5 Motion of central force 163
Questions 168
Bibliography 169