- 01-166 Ulrich Mutze
- Predicting Classical Motion Directly from the Action Principle III
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.