Matrix equations of the motion of multibody systems in hamiltonian variables. Systems with a tree structure

The article is devoted to the development of methods for computer simulation of dynamics of mechanical systems. The article presents a new matrix form of equations of motion for rigid body systems with a tree structure and holonomic constrains. Generalized coordinates and impulses were exploited as independent parameters that uniquely identified the configuration and velocity distribution of bodies. The most important features of the equations are that they are resolved with respect to derivatives of generalized impulses and don’t contain constraint forces. In this paper we obtain the equations on the base of the Hamilton-Ostrogradsky principle and matrix-geometric approach. The method is intended for the study of motions of mechanical systems with the usage of computers. Recurrent formulae were obtained for all kinematic and dynamic variables that were included in the equations. An example demonstrates all stages of source data preparation and construction of specific equations in the proposed form for a mechanical system with six degrees of freedom.