一、課程簡介:
1. Mechanics of a System of Particles
constraints
D’Alembert’s Principle and Lagrange’s equations
2. Variational Principles and Lagrange’s Equations
calculus of variation and Hamilton’s principle
Lagrange multipliers and nonholonomic systems
symmetry and conservation theorems in Lagrangian formulation
3. The Two-body Central Force Problem
equivalent one-dimensional problem and reduced mass
virial theorem
differential equation for the orbit, integrable power-law potentials
conditions for closed orbits (Bertrand’ theorem)
Kepler problem: Inverse square law of force
Laplace-Runge-Lenz vector
Scattering in a central force field
4. The Kinematics of Rigid Body Motion
rotation matrix and rotation group
Euler angles
Euler’s theorem on the motion of a rigid body
Infinitesimal and Finite rotations
the Coriolis force
5. The Rigid Body Equations of Motion
rotational tensor
inertia tensor and moment of inertia, principal axis transformation
Euler equations of motion
torque-free motion of a rigid body
heavy symmetrical top with one point fixed
Precession of the equinoxes and satellite orbits
6. Small Oscillations
formulation, eigenvalue equation and the principal axis transformation
normal modes
free vibrations of a linear triatomic molecule
forced vibrations and dissipative forces

二、先修課程:

三、參考書目:`Classical Mechanics` by Goldstein