Computational efficiency analysis matrix equations of motion for systems of rigid bodies with a tree structure in Hamiltonian variables
Abstract
Computational efficiency analysis matrix equations of motion for systems of rigid bodies with a tree structure in Hamiltonian variables
Incoming article date: 13.06.2023Methods of computer formation of the equations of motion of multibody systems with a tree structure and algorithms for their reduction to the normal form of ordinary differential equations are considered. The equations of motion are written using Hamilton's formalism for an extended set of state variables of a mechanical system. The equations are presented in a compact visual form. Recursive formulas for determining all coefficients of equations are written out. Algorithms for reducing these equations to Hamilton equations in generalized coordinates and generalized momenta are presented. An algorithm for solving the obtained equations of motion for multibody systems using the LTDL-elimination is presented. Formulas are written that allow one to calculate the amount of arithmetic operations required to bring the equations of motion to normal form using the considered algorithms. On the basis of these formulas, a comparative analysis of the efficiency of algorithms for rigid bodies systems of various structures and with various types of connections between bodies is carried out. The results of the analysis are presented in the form of diagrams. The diagrams highlight areas in which the advantage of one or another method is manifested, depending on the type of mechanical system.
Keywords: multibody systems, equations of motion, dynamics, canonical momenta, mathematical modeling, computational efficiency