高等動力學
Advanced Dynamics
| 節 | 週二 |
|---|---|
A 18:30–19:20 | 高等動力學 EE229（光復） 3 節連堂 |
B 19:30–20:20 | |
C 20:30–21:20 |
* 根據陽明交大上課時間表所列
對分析動力學及三維剛體動力學有堅實的知識及深入的理解,俾能對有關的各種工程及理論問題之解決,有門徑可依。
應用力學(二):動力學
無備註
課堂講授
1. 不得無故缺課 (20%) 2. 每章習題必須按時交 (20%) 3. 期中考試一次,期末報告一篇(各30%)
Survey of the Elementary Principles
Constraints, D’Alembert’s Principle and Lagrange’s Equation, Velocity-Dependent Potentials and the Dissipation Function, Variational Principles and Lagrange’s Equations.
- 講授：
- 6
Variational Principles and Lagrange’s Equations
Hamilton’s Principle, Derivation of Lagrange’s Equations from Hamilton’s Principle, Extension of Hamilton’s Principle to Nonholonomic Systems, Conservation Theorems and Symmetry Properties.
- 講授：
- 6
The Central force Problem
The Equations of Motion and First Integrals, The Virial Theorem, The Laplace-Runge-Lenz Vector.
- 講授：
- 6
The Kinematics of Rigid Body Motion
Orthogonal Transformations, Formal Properties of the Transformation Matrix, The Euler Angles, The Cayley-Klein Parameters and Related Quantities, Euler’s Theorem on the Motion of a Rigid Body, Finite Rotations, Infinitesimal Rotations.
- 講授：
- 6
The Rigid Body Equations of Motion
Angular Momentum and Kinetic Energy of Motion about a Point, Tensors, The Inertia Tensor and the Moment of Inertia, Solving Rigid Body Problems and the Euler Equations of Motion, Torque-free Motion of a Rigid Body, The Heavy Symmertrical Top with One Point Fixed.
- 講授：
- 6
The Hamilton Equations of Motion
Legendre Transformations and the Hamilton Equations of Motion, Cyclic Coordinates and Conservation Theorems, Routh’s Equations, The Principle of Least Action.
- 講授：
- 6
Canonical Transformations
The Equations of Canonical Transformation, The Symplectic Approach to Canonical Transformations, Poisson Brackets and Other Canonical Invariants, Equations of Motion, Infinitesimal Canonical Transformations, and Conservation Theorems in the Poisson Bracket Formulation, Liouville’s Theorem.
- 講授：
- 6
備註：期中考
Hamilton-Jacobi Theory and Action-Angle Variables
The Hamilton-Jacobi Equation for Hamilton’s Principal Function, The Hamilton-Jacobi Equation for Hamilton’s Characteristic Function, Separation of Variables in the Hamilton-Jacobi Equation, Ignorable Coordinates and the Kepler Problem, Action-Angle Variables for Completely Separable Systems, The Kepler Problem in Action-angle Variables.
- 講授：
- 6
Chaos and Canonical Perturbation Theory
Perturbations and the Kolmogorov-Arnold-Moser Theorem, Chaotic Trajectories and Liapunov Exponents, Poincare Maps, Bifurcations, Driven-damped Harmonic Oscillator, Parametric Resonance, Fractals and Dimensionality, Time-dependent Perturbation Theory, Illustrations of Time-dependent Perturbation Theory.
- 講授：
- 6
備註：期末報告
| 週次 | 主題 |
|---|---|
| 第 1 週 | Constraints, D’Alembert’s Principle and Lagrange’s Equation. 9/12 |
| 第 2 週 | Velocity-Dependent Potentials and the Dissipation Function, Variational Principles and Lagrange’s Equations. 9/19 |
| 第 3 週 | Hamilton’s Principle, Derivation of Lagrange’s Equations from Hamilton’s Principle. 9/26 |
| 第 4 週 | Extension of Hamilton’s Principle to Nonholonomic Systems, Conservation Theorems and Symmetry Properties. 10/3 |
| 第 5 週 | The Equations of Motion and First Integrals. 10/10 |
| 第 6 週 | The Virial Theorem, The Laplace-Runge-Lenz Vector. 10/17 |
| 第 7 週 | Orthogonal Transformations, Formal Properties of the Transformation Matrix. 10/24 |
| 第 8 週 | The Euler Angles, The Cayley-Klein Parameters and Related Quantities, Euler’s Theorem on the Motion of a Rigid Body, Finite Rotations, Infinitesimal Rotations. 10/31 |
| 第 9 週 | Angular Momentum and Kinetic Energy of Motion about a Point, Tensors, The Inertia Tensor and the Moment of Inertia. 11/07 |
| 第 10 週 | Solving Rigid Body Problems and the Euler Equations of Motion, Torque-free Motion of a Rigid Body, The Heavy Symmertrical Top with One Point Fixed. 11/14 |
| 第 11 週 | Legendre Transformations and the Hamilton Equations of Motion, Cyclic Coordinates and Conservation Theorems. 11/21 |
| 第 12 週 | Routh’s Equations, The Principle of Least Action. 11/28 |
| 第 13 週 | The Equations of Canonical Transformation, The Symplectic Approach to Canonical Transformations, Poisson Brackets and Other Canonical Invariants. 12/5 |
| 第 14 週 | Equations of Motion, Infinitesimal Canonical Transformations, and Conservation Theorems in the Poisson Bracket Formulation, Liouville’s Theorem. 12/12 |
| 第 15 週 | The Hamilton-Jacobi Equation for Hamilton’s Principal Function, The Hamilton-Jacobi Equation for Hamilton’s Characteristic Function, Separation of Variables in the Hamilton-Jacobi Equation. Ignorable Coordinates and the Kepler Problem, Action-Angle Variables for Completely Separable Systems, The Kepler Problem in Action-angle Variables. 12/19 |
| 第 16 週 | Ignorable Coordinates and the Kepler Problem, Action-Angle Variables for Completely Separable Systems, The Kepler Problem in Action-angle Variables. 12/26 |
| 第 17 週 | Perturbations and the Kolmogorov-Arnold-Moser Theorem, Chaotic Trajectories and Liapunov Exponents, Poincare Maps, Bifurcations, Driven-damped Harmonic Oscillator, Parametric Resonance. 1/02 |
| 第 18 週 | Fractals and Dimensionality, Time-dependent Perturbation Theory, Illustrations of Time-dependent Perturbation Theory. 1/09 |
H. Goldstein, C. Poole, J. Safko, Classical Mechanics, Third Edition, 2002, Addison Wesley, New York.
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- 1. 04-24961123ext.1402;04-24961100ext.6700;0920795361 2. E-mail: kanechen@so-net.net.tw;kane@mail.hust.edu.tw