Computer Calculation of Mechanisms Involving Intermittent Motions

摘要

This paper deals with a simple computational approach to the analysis of dynamical systems involving intermittent motion in which the velocities involved can be discontinuous due to impulsive forces, impact, mass capture, and mass release. The sequence of these events may not be known ahead of time, and may in fact be one of the things we wish the computer to determine. The dynamical equations are formulated using a logical function method due to P. Ehle. The resulting system of ordinary differential equations with discontinuous coefficients is integrated using a standard computer code in regions where the coefficients are continuous. When discontinuities occur, jump conditions across the discontinuity are used to express the new velocities in terms of the old, and the ordinary differential equation solver is simply restarted with new initial conditions. To illustrate the simplicity of the approach, the method is applied to a dynamical system of ten masses considered by Ehle. The computer code and numerical results are included. (Author)