9 - Dynamics of Particles and Rigid Bodies

Abstract

The chapter reviews fundamental theories, formulas, solution methods, and a set (toolbox) of MATLAB functions for dynamics of particles and rigid bodies. When a particle moves along a path in a reference frame, its position is described by a position vector, which is a function of time. The motion (position, velocity, and acceleration) of a particle can be described in different coordinates, but two commonly used coordinate systems are rectangular Cartesian coordinates and cylindrical coordinates. A particle is subject to a force that is always directed toward a fixed point O. Such a force is called the central force, and O the center of force. The moment of a central force about the center is always zero. So, the angular momentum of a particle moving under a central force is constant. A rigid body is an object in which the distance between any two points remains the same. The chapter presents two-dimensional motion of slablike rigid bodies and a toolbox that has a function—massmin—for computing mass moments of inertia of the bodies.