On the numerical solution of differential/algebraic equations of motion of deformable mechanical systems with nonholonomic constraints

Abstract

The Lagrange Multipliers method can be employed in deriving differential/algebraic equations of motion of deformable multibody systems subject to holonomic and/or nonholonomic (sceleronomic or rehonomic) constraints. The resulting dynamic equations of motion are highly nonlinear due to large rotations of the multibody system components. The system differential equations and holonomic and nonholonomic constraint equations represent a linear system of algebraic equations in the accelerations and Lagrange multipliers. Since the existence of a closed form solution is, in general, impossible, numerical methods and approximation techniques are employed in numerical integration of the resulting accelerations. In this paper two numerical algorithms for the computer aided analysis of deformable systems subject to nonholonomic constraint equations are discussed and compared.