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課程名稱 |
古典力學
Classical Mechanics |
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開課學期 |
106-1 |
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授課對象 |
理學院 物理學研究所 |
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授課教師 |
陳義裕 |
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課號 |
Phys7019 |
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課程識別碼 |
222 M1940 |
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班次 |
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學分 |
4.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三6,7(13:20~15:10)星期五6,7(13:20~15:10) |
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上課地點 |
新物112新物112 |
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備註 |
總人數上限：90人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1061Phys7019_ |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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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. |
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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
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課程要求 |
Grading Policy:
Homework: 40%
Midterm: 30%
Final Exam: 30%
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Textbook:
Herbert Goldstein, Charles P. Poole, and John L. Safko, Classical Mechanics, 3rd ed, Pearson (2001).
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參考書目 |
None. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Midterm Exam |
30% |
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2. |
Final Exam |
30% |
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3. |
Homework |
40% |
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