Dynamics of a Particle
This chapter contains a detailed treatment of the dynamics of a particle. The main emphasis is on obtaining and solving the equations of motion when the particle is subject to constraints. In most cases the solution will be obtained numerically using MATLAB®. Both Newton-Euler and Lagrangian methods are used to obtain the equations of motion. Constraints are handled by either embedding them into the equations of motion (implicitly or explicitly) or solving an augmented system of equations that also yields an explicit expression for the constraint forces. Both ideal and nonideal constraints are considered. Issues that must be addressed when solving the equations of motion numerically are discussed, including the problem of constraint drift.