|
週次 |
日期 |
單元主題 |
|
第1週 |
|
Dynamics of Particles -
1.1 Space and Time
1.2 Euclidean Geometry and Vector Space
1.3 Kinematics of Particles |
|
第2週 |
|
Dynamics of Particles -
1.4 Newton’s Law
1.5 Balance Laws of Motion of a Particle
1.6 Simple Pendulum in Plane Motion |
|
第3週 |
|
Dynamics of Particles -
1.7 The Law of Universal Gravitation and Planetary Motion
1.8 Motion of a System of Particles
1.9 Many Body Problems |
|
第4週 |
|
Dynamics of Particles -
1.10 Transformation of Cartesian Coordinates
1.11 Motion Relative to a Moving Coordinate System
1.12 Motion Near the Surface of the Earth |
|
第5週 |
|
Dynamics of Rigid Continuum -
2.1 Specifications of Continua
2.2 Laws of Mechanics for a Continuum
2.3 Kinematics and Finite Rotation of a Rigid Body |
|
第6週 |
|
Dynamics of Rigid Continuum -
2.4 Kinetics of a Rigid Body
2.5 Representations of Rotational Motion
2.6 Motion of a Top - Eulerian Approach |
|
第7週 |
|
Dynamics of Rigid Continuum -
2.7 Gyroscopes and Accelerometers
2.8 Sliding, Rolling, and Collision of Rigid Bodies |
|
第8週 |
|
Principles of Mechanics -
3.1 History of Classical Mechanics (from 1600 to 1900)
3.2 Principle of Statics |
|
第9週 |
|
Principles of Mechanics -
3.3 D’Alembert’s Principle
3.4 D’Alembert-Lagrange’s Equation for Holonomic Systems |
|
第10週 |
|
Principles of Mechanics -
3.5 Lagrange’s equations for Holonomic Systems
3.6 Motion of a dumb-bell shaped satellite |
|
第11週 |
|
Principles of Mechanics -
3.7 Cyclic Coordinates and Spinning Top (Lagrangian Approach)
3.8 D’Alembert-Lagrange Equations for Non-holonomic Systems |
|
第12週 |
|
Principles of Mechanics -
3.9 Rolling of Two Wheels Connected by an Axle on an Inclined Plane
3.10 Jourdain’s Variational Equation and Appell-Kane Method |
|
第13週 |
|
Hamiltonian Dynamics -
4.1 Element of Calculus of Variations
4.2 Hamilton’s Principle |
|
第14週 |
|
Hamiltonian Dynamics -
4.3 Legendre Transformation
4.4 Hamiltonian Equations |
|
第15週 |
|
Hamiltonian Dynamics -
4.5 Hamiltonian and Conservation Laws
4.6 Raileigh’s Dissipation Function |
|
第16週 |
|
Hamiltonian Dynamics -
4.7 Canonical Transformation and Hamilton-Jacobi Equation
4.8 The Electromagnetic Force |
|
第17週 |
|
Hamiltonian Dynamics -
4.9 Lagrangian and Hamiltionian for the Dynamics of a Charged Particle Moving in an Electromagnetic Field
4.10 Gauss’ Principle of Least Constraint |