國立交通大學課程綱要
開課單位
電子物理系
課程名稱
英文名稱
古典力學 1
學 分 數
3 學分
授課教師
儒森斯坦
授課學期
96 學年度
1 學期
人數上限
Classical Mechanics I
上課時數 3 小時
先修課程 理論力學
課程目標：介紹光電工程之基本原理及其應用,作為光電科技之入門學程
1. To deepen the knowledge of classical mechanics in order to help with understanding of quantum and
statistical mechanics. Basic notions like Lagrangian, Hamiltonian, symmetries, conservation laws and
logical relation between them, all necessary for understanding of quantum mechanics and statistical
physics are introduced and their origin explained. The course doesn’t include physics of rotation,
relativity and scattering.
2. First part contains the description of solvable models including the Kepler’s solution. The second part
concentrates on nonlinear dynamics. Basic notions of state space, fixed point, cycle, bifurcation, chaos and
others are introduced.
課程綱要：
I. Conservation laws and integrable systems
A.
1.
2.
B.
1.
2.
C.
1.
2.
Conservation of energy (2h, MT chapter 2.5).
Conservative forces and their potential energy.
Example of a nonconserved force.
One dimensional motion (3h, MT 2.6).
Solution for the periodic motion between two turning points.
Period.
Central forces and angular momentum conservation (4h, MT 8.1-8.3).
Definition of angular momentum. Tensors.
Angular momentum conservation.
D. Solution of the Newton equation for particle moving in the field of central force (3h MT 8.4-8.6).
1. How many conservation laws has a particle in the field of central force?
2. First use of angular momentum conservation. Reduction 3D to 2D.
3. Second use of Orbital momentum. 2D to 1D.
4. Energy conservation and solution.
5. Orbits and their periodicity.
E. Kepler’s problem (2h MT 8.7)
II. Nonintegrable systems. Basic phenomena.
A. The state space and fixed points (1h, S 2).
B. One dimensional state space. (2h, S 3)
1.
Exact solution and fixed points.
2.
Lyapunov exponents.
3.
Bifurcations.
C. The d=2 state space. Cycles (4h, S 5-7).
1.
Fixed points in d=2.
2.
Complete classification of fixed points in 2d.
3.
Discovery of nonlinear oscillations.
4.
Stable manifolds in the Hopf system.
5.
Hopf bifurcation.
D. Cycles and the 1d maps (1h, S 7).
1.
Poincare section and its map.
2.
Classification of cycles.
III. Chaos
A. The d=3 state space. (2h, S 9).
1.
What is new in 3d?
2.
Fixed points.
3.
3d cycles and 2d Poincare maps.
4.
Bifurcations in cycles: period doubling.
B. The period doubling route to chaos (2h, S 10).
1.
Discovery of chaos.
2.
The Rossler system.
3.
Logistic map. Explanation of the period doubling route to chaos.
C. Strange (fractal) attractors (6h, S 11,12).
1.
Analysis of the Lorentz system.
2.
Sets of fractional dimensionality.
3. The Lorentz strange attractor and the 2d Henon map.
4. How the intermittency chaos strange attractor works. The pastry picture.
教科書: J. Marion and S. Thornton (MT) “Classical dynamics of particles and systems”,
Saunders College, NY, 1995.
S. Strogartz (S) “Nonlinear dynamics with applications to physics, biology, chemistry and
engineering”, Addison-Wesley, Taipei, 1994.
參考書目：
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