New algorithm applied to vibration equations of time-varying system

Vibration equations of time-varying system are transformed to the form which is suitable to precise integration algorithm. Precision analysis and computation efficiency of new algorithm are implemented. The following conclusions can be got. Choosing matrixes M, G and K is certainly flexible. We can place left side of nonlinear terms of vibration equations of time-varying system into right side of equations in precise integration algorithms. The key of transformation from vibration equations of time-varying system to first order differential equations is to form matrix H, which should be assured to be nonsingular. With suitable disposal, precision and computation efficiency of precise integration algorithms are greatly larger than those of general methods.