Dynamics of Elastic Multibody Systems Involving Closed Loops

Abstract

A formalism for investigation of an arbitrary system of bodies, interconnected by joinjs with arbitrary (holonomic, nonholonomic, scleronomic or rheonomic) constraints is presented. This formalism extends the ideas developed in [1,2,3,4] for systems of rigid bodies. It considers systems of flexible bodies, as well. The state variables include generalized coordinates characterising the bodies’ attitudes, nonholonomic variables characterising their velocities and a finite number of deformation coordinates representing the deformation fields of the bodies. Special attention is devoted to the attainment of an full description of the structure of the interconnections in the system and to the compact expression of the constraint equations due to the existence of closed loops. Thus, the formulation of the equations of motion is easily completed. The equations of motion are being derived from the variational principles of mechanics [5], while the emphasis is on the principle of Jourdain (the principle of virtual power) add the principle of Gauss.The mathematical apparatus employed is convenient for algorithmization and can be easily developed into numerical algorithms for implementation in computer programmes.