課程資訊

Classical Mechanics

106-1

Phys7019

222 M1940

4.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061Phys7019_

This course discusses the more advanced aspects of some of the topics covered in intermediate Mechanics one learns in a regular undergraduate physics curriculum.

Outline of Contents:
(Not necessarily to be strictly followed.) An * indicates a topic that might be omitted if time does not permit.

1. Variational principles and the Lagrangian formulation:
From F=ma to a variational formulation
The Lagrangian formulation
Taking special relativity into account
Constraints: holonomic and nonholonomic
D’Alembert’s principle
Symmetries and conservation theorems

2. The central force problem:
Reducing a two-body problem to an equivalent one-body problem
Bertrand’s theorem
Kepler’s problem
The Laplace-Runge-Lenz vector
Kindergarten three-body problem
Scattering

3. Rigid body motion:
Describing rotations
The Coriolis effect
The inertia tensor
Motion of a symmetric top
How does a cat manage to land on its feet

4. Small oscillations:
Normal modes
A taste of “inverse problems”

5. The Hamiltonian formulation:
From Lagrangian to Hamiltonian equations of motion
Routh’s procedure
The Hamiltonian formulation of relativistic mechanics
Variational principle directly associated with the Hamiltonian
formulation
The principle of least action

6. Canonical transformations:
Canonical transformations and the symplectic approach
Poisson brackets
Liouville’s theorem and other Poincare’s integral invariants

7. Hamilton-Jacobi theory and action-angle variables:
The Hamilton-Jacobi formulation
Separation of variables
Action-angle variables
The Kepler problem in action-angle variables

8. A little bit of chaos*:
A brief account of the KAM-theorem
Helon-Heiles Hamiltonian
The logistic equation and simple bifurcation theory
Fractals

9. Canonical perturbation theory:
Time-dependent perturbation theory
Time-independent perturbation theory
Adiabatic invariants and the old quantum theory

10. Continuous systems:
The transition from discrete to continuous
The Lagrangian formulation of continuous systems
The stress-energy tensor and conservation theorems
Hamiltonian formulation
Noether’s theorem

11. Linear elasticity*:
The strain and the stress tensors
Lame coefficients and some elastic moduli
Simple accounts of waves in isotropic media

Grading Policy:
Homework: 40%
Midterm: 30%
Final Exam: 30%

Office Hours

None.

Textbook:
Herbert Goldstein, Charles P. Poole, and John L. Safko, Classical Mechanics, 3rd ed, Pearson (2001).

(僅供參考)

 No. 項目 百分比 說明 1. Midterm Exam 30% 2. Final Exam 30% 3. Homework 40%

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