高等動力學

1 INTRODUCTORY CONCEPTS  Laws of Motion for a Particle  D’Alembert’s Principle 2 KINEMATICS OF PARTICLE  Angular Velocity  Rigid Body Motion about a Fixed Point  Tangential and Normal Components  Velocity and Acceleration of a Point in a Rigid Body  Vector Derivatives in Rotating Systems  Motion of a Particle in a Moving Coordinate System  Plane Motion and The Instantaneous Center 3 DYNAMICS OF A PARTICLE  Simple Example of Particle Motion  Work and Kinetic Energy  Conservative Forces  Linear Impulse and Momentum  Angular Impulse and Momentum  Coulomb Friction 4 DYNAMICS OF A SYSTEM OF PARTICLES  System of Particles  Work and Kinetic Energy  Linear Impulse and Momentum  Angular Impulse and Momentum  Collisions  Collisions with Friction  Rocket Problem 5 ELEMENTARY PERTURBATION THEORY 6 LAGRANGE’S EQUATIONS  Degrees of Freedom  Generalized Coordinates  Constraints  Virtual Work  D’Alembert’s Principle  Generalized Forces  Generalized Momentum  Derivation of Lagrange’s Equations  Lagrange Multipliers  Conservative Systems 7 BASIC CONCEPTS AND KINEMATICS OF RIGID BODY MOTION  Degrees of Freedom for a Rigid Body  Moments of Inertia  Kinetic Energy  Dyadic Notation  Translation of Axes  Rotation of Axes  Axis and Angle of Rotation  Ellipsoid of Inertia  Reduction of Forces  Infinitesimal Rotations  Eulerian Angles  Center of Percussion  Work 8 DYNAMICS OF A RIGID BODY MOTION  Equations of Motion for a Rigid Body  Rotational Equations  Systems of Rigid Bodies  Rotational Equations Using Euler Angles  Generalized Momentum  Free Rotational Motion  Free Rotational Motion of an Axially Symmetric Body  Motion of a Top  Modified Euler Equations  D’Alembert’s Principle and Rigid Body  Gravitational Moments  Euler Parameters 9 VIBRATION THEORY  Conditions for Equilibrium  Kinetic Energy  Quadratic Forms  Free Vibrations of a Conservative System  Use of Symmetry

Dynamics

Homework 30% Midterm Exam. 30% Final Exam. 30%

PRINCIPLES OF DYNAMICS, Donald T. Greenwood, Second Edition, 1988 by Prentice-Hall, Inc. CLASSICAL DYNAMICS, Donald T. Greenwood, 1977 by Prentice-Hall, Inc.