Abstract
In a time history analysis of multibody system, time step size in numerical integration has to be appropriately decided to keep accuracy and stability. As they are controlled by the product of step size and the absolute maximum eigenvalue of the system, it is important to investigate the eigenvalues. In this paper an eigenvalue equation is derived and solved for typical models of nonlinear multibody system with Baumgarte's constraints, then the effect of its eigenvalues to the stability is confirmed by a time history analysis. As a conclusion it is found that (1) Eigenvalues are obtained by a linearized equation , and they can be used to evaluate the stiffness of a system. (2) Baumgarte's constraints expressed as Φ+2αΦ+β^2Φ=0 have the eigenvalues which equal the roots of the characteristic equation s^2+2αs+β^2=0. When α=β, its mode has the critical damping, which means the constraint errors reduce fast, so it is recommended that α=β. (3) As the eigenvalues come from Baumgarte's constraints affect the numerical stability as well as the physical one. The values α(=β) are desirable to be large, but less than the maximum physical eigenvalue.
