課程概述 |
Outline:
I. Newtonian Dynamics
Kinematics of Particle, Newton's Laws, Conservation Theorems, Simple Pendulum Problems, Motion in Central Force Field, Motion of System of Particles
II. Dynamics of a Rigid Body
Kinematics of Rigid Body, Rotation of Coordinate System in Space,
Rotation of Vector in Space, Motion relative to a Moving Coordinate System
Motion on the Surface of Earth, Dynamic Specification of a Rigid Body, Equations of Motion, Motion of a Top, Sliding and Rolling of Rigid Bodies,
III. Lagrangian Dynamics
Constraints and Generalized Coordinates, Principle of Virtual Work, D'Alembert's Principle, Lagrangian Equation for Holonomic Systems, Lagrangian Equations for Non-holonomic Systems, Cyclic Coordinates and Routh's Method,
IV. Hamiltonian Dynamics
Calculus of Variations, Hamilton's Principle, Legendre's Transformation, Hamilton's Equations, Hamiltonian and Conservation Laws, Poisson brackets, Canonical transformation, Hamilton-Jacobi equation, Modern Dynamics
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