01-166 Ulrich Mutze

Predicting Classical Motion Directly from the Action Principle III (97K, PostScript) May 4, 01

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Abstract. For an arbitrary holonomic mechanical system a method for constructing time-discrete trajectories is derived by applying a generalized principle of stationary action to the manifold of those system paths which are parabolic with respect to system of generalized coordinates. The method is applied to the anti-damped harmonic oscillator, and data are reported that suggest that the method accurately represents the growth of the amplitude till numerical overflow. A modified variational derivative of the generalized action integral is shown to agree with the force that the environment of the system exerts to it. This generalizes the characterization of free motion in terms of vanishing variational derivative.

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