Formulation of dynamical equations of motion

Abstract

Advances in computer technology have brought into reach the solutions of many dynamics problems previously regarded as excessively complex. However, in order actually to carry out solutions, one must be able to generate computational algorithms in an effective way. In the present paper, this issue is confronted through the discussion of a law of motion that is, in essence, a generalization of Lagrange’s equations. Following the introduction of ‘‘generalized speeds,’’ ‘‘partial angular velocities,’’ and ‘‘partial velocities,’’ the equations of motion are formulated for a simple system in order to illustrate each of these concepts in concrete terms. To provide a basis for comparisons, the equations of motion of the system are then formulated also by employing Lagrange’s equations.