Algorithms for solving the equations of motion with Poisson impulses of multibody systems with tree structure

The article presents the new matrix form the equations of motion with generalized coordinates and Poisson impulses of multibody systems with tree structure. Two algorithms solve these equations for senior derivatives focused on the use of computers are offered. The first algorithm is a method of Chaser for solving the systems of linear algebraic equations. The second algorithm uses the Cholesky factorization schema. Recurrent formulas are obtained for all kinematic and dynamic variables that are included in the equation. The time complexity of solution of equations using data algorithms grows on linear depending with the number of bodies in a mechanical system that testifies to their effectiveness. Proposed algorithms are compared. For examples of integrating the equations of motion of systems of bodies with a large number of degrees of freedom shows the advantage of algorithm based Cholesky decomposition schema.