課程資訊
課程名稱
古典力學
Classical Mechanics 
開課學期
106-1 
授課對象
理學院  天文物理研究所  
授課教師
陳義裕 
課號
Phys7019 
課程識別碼
222 M1940 
班次
 
學分
4.0 
全/半年
半年 
必/選修
選修 
上課時間
星期三6,7(13:20~15:10)星期五6,7(13:20~15:10) 
上課地點
新物112新物112 
備註
總人數上限:90人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061Phys7019_ 
課程簡介影片
 
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課程概述

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

課程目標
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
 
課程要求
Grading Policy:
Homework: 40%
Midterm: 30%
Final Exam: 30%
 
預期每週課後學習時數
 
Office Hours
 
參考書目
None. 
指定閱讀
Textbook:
Herbert Goldstein, Charles P. Poole, and John L. Safko, Classical Mechanics, 3rd ed, Pearson (2001).
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Midterm Exam 
30% 
 
2. 
Final Exam 
30% 
 
3. 
Homework 
40% 
 
 
課程進度
週次
日期
單元主題