Multiscale Methods for Stiff and Constrained Mechanical Systems

We suggest multiscale methods for the integration of systems of second-order ordinary differential equations (ODEs) whose solutions include components that oscillate with large frequencies and small amplitudes. The methods do not need to integrate completely the fast oscillations and may employ step-sizes determined by the rate of change of the slow motions of the system. The technique may be used with any standard ODE method with fixed step-size and also in conjunction with off-the-shelf, variable-step ODE software. Alternatively, the ideas presented here may be used to integrate constrained mechanical systems by means of conventional ODE codes.

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