Implicit Reduced Involutive Forms and Their Application to Engineering Multibody Systems

Abstract. The RifSimp package in Maple transforms a set of differential equations to Reduced Involutive Form. This paper describes the application of RifSimp to challenging real-world problems found in engineering design and modelling. RifSimp was applied to sets of equations arising in the dynamical studies of multibody systems. The equations were generated by the Maple package Dynaflex, which takes as input a graph-like description of a multibody mechanical system and generates a set of differential equations with algebraic constraints. Application of the standard RifSimp procedure to such Differential Algebraic Equations can require large amounts of computer memory and time, and can fail to finish its computations on larger problems. We discuss the origin of these difficulties and propose an Implicit Reduced Involutive Form to assist in alleviating such problems. This form is related to RifSimp form by the symbolic inversion of a matrix. For many applications such as numerically...

• Type: Conference
• Year: 2004
• Where: GIAE
• Authors: Wenqin Zhou, David J. Jeffrey, Gregory J. Reid, Chad Schmitke, John McPhee
• Keywords: Differential Equations, Equations, GIAE 2004, Involutive Form, Mathematics