Development and Application of a Generalized d’Alembert Force for Multifreedom Mechanical Systems

Abstract

A set of expressions termed the generalized d’Alembert force is determined for application to two and three-dimensional dynamic analysis of discrete, nonlinear, multifreedom, constrained, mechanical dynamic systems. These expressions greatly simplify the task of developing a correct set of second order differential equations of motion for mechanical systems which are nonlinear because of large deflections or other geometric effects. They apply to both constrained and unconstrained mechanical systems via the method of Lagrange equations with constraint. The two-dimensional version of the expressions has been successfully applied in a type-varient computer program for the dynamic analysis of mechanical networks, and example problems simulated with this program are discussed.