The quasi-variational principles of rigid-body dynamics and their applications

The Reference 1 points out that recent studies to solvethe problems of flexible multi-body dynamics mainly depend on the numerical,quantitative methods and almost no one involves in the analytical discussiondue to the complexity of flexible multi-body configuration. It isunfavorable to profoundly understand the essence of nonlinear mechanics ofthe system and to predict the feature of overall dynamics of the system.Therefore, it is the need to study theoretical analysis of flexiblemulti-body system. Of course, this is a very complex problem and it takes avery long time to solve this problem. The research of this papercarries out to adapt this need.For flexible multi-body, if we think that external forces on the deformablebody (including body force and surface force) are non-conservative forces,which also lead to non-conservative forces on the rigid body, that is, theresultant force and the resultant couple acting on center of mass arenon-conservative generalized forces. This research is to apply thequasi-variational principles of non-conservative system to the theoreticalanalysis of the flexible multi-body dynamics. Because of the complexity ofthe problem, it is divided into several sub-tasks: 1. To study thequasi-variational principles of rigid-body dynamics and their applications.This is the main subject of this paper; 2. To study the quasi-variationalprinciples of flexible single-body dynamics and their applications. Thissubject has been published in ``Science in China''; 3. To study the quasi-variational principles of flexible multi-body dynamics and theirapplications. This subject has been written in Ph.D. thesis.In this paper, the quasi-variational principles of rigid-body dynamics areestablished. The quasi-stationary conditions of the quasi-variationalprinciples of rigid-body dynamics are deduced. The generalizedquasi-variational principles of rigid-body dynamics are established. Theapproach to seek analytical solution and numerical solution of rigid-bodydynamics is illuminated by using generalized quasi-variational principles.Finally, the advantage of applying variational methods to the study of therigid-body dynamics is validated by calculation examples.