Matrix equations of motion for multibody systems in hamiltonian variables. Closed chain systems

The article deals with the development of methods for computer simulation of mechanical systems dynamics. It presents a new matrix form of equations of motion for rigid body systems with closed kinematic chains and holonomic constraints. The equations are presented in Hamiltonian variables. A feature of the system of equations is that it is resolved with respect to derivatives of generalized impulses and does not contain constraint forces. The method is intended for the study of motions of mechanical systems with the use of computers. Recurrent formulae were obtained for all kinematic and dynamic variables included in the equations. Using the example of one mechanical system, there are demonstrated all stages in the preparation of primary information for composing equations of motion in the proposed form.