Advanced Dynamics Course

约 223 个字 预计阅读时间 1 分钟

Analytical Mechanics (16 class hours)

Week 1: Introduction, Lagrange's Equations of a Particle lecture-01

Week 2: Constraints, Generalized Coordinates, Degrees of Freedom and Configuration Space, Virtual Displacement and Virtual Work lecture-02

Week 2: D’Alembert’s Principle and Lagrange's Equations

Week 3: Calculus of Variations, Euler's Equation, Hamilton's Principle

Week 4: Geodesics, Lagrange's Equations for Constrained Systems Week 4: Nonholonomic Systems, Cyclic Coordinates, Generalized Momentum, Generalized Energy, Conservation Laws

Week 5: Noether's Theorem, Hamilton's Canonical Equations Week 6: Hamilton's Canonical Equations, Poisson Brackets

Advanced Dynamics Course Content

Module	Class Hours	Week	Content
Vibration Theory	6	6	Multi-Degree-of-Freedom Vibration Systems
Vibration Theory	6	7	Natural Frequencies, Mode Shapes, Principal Coordinates
Vibration Theory	6	8	Vibration and Waves, Forced Vibration
Rigid Body Kinematics	6	8	Midterm Examination
Rigid Body Kinematics	6	9	Exam Paper Review, Rigid Body Kinematics: Velocity and Angular Velocity
Rigid Body Kinematics	6	11	Euler Angles
Rigid Body Kinematics	6	12	Euler-Rodrigues Rotation Formula, Quaternions
Rigid Body Dynamics	10	12	General and Fixed-Point Motion of a Rigid Body, Inertia Tensor
Rigid Body Dynamics	10	13	Euler's Equations
Rigid Body Dynamics	10	14	Free Rotation of a Rigid Body
Rigid Body Dynamics	10	14	Gyroscopic Motion
Rigid Body Dynamics	10	15	Euler's Disk
Rigid Body Dynamics	10	16	Final Examination