Theoretical Mechanics

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Table of Contents

Chapter 1 Kinematics of Particles
1.1 Description of the particle motion
l.2 Representation of velocity and acceleration in components

Chapter 2 Dynamics of Particles
2.1 Basic laws of dynamics
2.2 Work and energy
2.3 Equation of motion
2.4 Velocity-dependent equation of motion
2.5 Position-dependent equation of motion
2.6 Inertial and non-inertial reference system, Galileo principle of relativity
2.7 Fundamental laws and conservation laws

Chapter 3 Mechanics of the particle group
3.1 Particle group
3.2 Theorem of momentum and conservation of momentum
3.3 Theorem of angular momentum and conservation of angular momentum
3.4 Theorem of kinetic energy and conservation of energy
3.5 Two-body problem
3.6 Center of mass coordinate and laboratory coordinate
3.7 Motion of the variable mass

Chapter 4 Mechanics of rigid body
4.1 Description of the rigid body motion
4.2 Vector of angular velocity
4.3 Euler angles
4.4 Motion equation of the rigid body
4.5 Principal axes transformation and inertia ellipsoid
4.6 Euler's equation of motion and symmetrical top
4.7 Motion in non-inertia system
4.8 Application of non-inertia system

Chapter 5 Analytical mechanics
5.1 Generalized coordinates and generalized force
5.2 Lagrangian equation
5.3 Variational principles of mechanics
5.4 Symmetry and conservation law
5.5 Lagrangian undetermined multiplies
5.6 Hamiltonian equations of motion
5.7 Canonical transformation, Hamilton-Jacobi equation
5.8 Poisson bracket, phase space and Liouville's theorem

Chapter 6 Central Force
6.1 Motion in central force field
6.2 Effective potential and general solutions
6.3 Inverse square law of force
6.4 Stability of orbits and perturbation
6.5 Motion of central force
Theoretical Mechanics