課程資訊

Dynamics

108-2

AM7021

543EM4010

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1082_Dynamics

This is a graduate-level course to introduce students the dynamics of particles and rigid bodies in this course. Topics covered in this course include: Dynamics of Particles, Dynamics of Rigid Continuum, Principles of Mechanics, and Hamiltonian Dynamics.

Upon completion, successful students will be able to understand the concepts of Lagrangian and Hamiltonian dynamics and how to apply the methods learnt from class to solve realistic dynamical systems.

Differential Equations, Linear Algebra, Statics

Office Hours

Slides along with any other materials related to the lecture will be posted on the class website.

Goldstein, Herbert, Charles P. Poole, and John Safko. Classical Mechanics. Pearson, 2013.

(僅供參考)

 No. 項目 百分比 說明 1. Homework 40% 2. Midterm Exam 30% 3. Final Exam 30%

 課程進度
 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