AN EFFECTIVE SOLVER FOR ABSOLUTE VARIABLE FORMULATION OF MULTIBODY DYNAMICS

This paper presents an effective and general method for converting the equations of motion of multibody systems expressed in terms of absolu te variables and Lagrange multipliers into a convenient set of equatio ns in a canonical form (constraint reaction-free and minimal-order equ ations). The method is applicable to open-loop and closed-loop multibo dy systems, and to systems subject to holonomic and/or nonholonomic co nstraints. Being aware of the system configuration space is a metric s pace, the Gram-Schmidt ortogonalization process is adopted to generate a genuine orthonormal basis of the tangent (null, free) subspace with respect to the constrained subspace. The minimal-order equations of m otion expressed in terms of the corresponding tangent speeds have the virtue of being obtained directly in a ''resolved'' form, i.e. the rel ated mass matrix is the identity matrix. It is also proved that, in th e case of absolute variable formulation, the orthonormal basis is cons tant, which leads to additional simplifications in the motion equation s and fits them perfectly for numerical formulation and integration. O ther useful peculiarities of the orthonormal basis method are shown, t oo. A simple example is provided to illustrate the convertion steps.