 03491 Ulrich Mutze
 A Simple Variational Integrator for General Holonomic Mechanical Systems
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Nov 7, 03

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Abstract. or an arbitrary holonomic mechanical system an integrator is derived by
applying an extended principle of stationary action
to the manifold of those system paths which are parabolic with respect to the system of
generalized coordinates under consideration.
A modified variational derivative of the action integral is shown to agree with the force
that the environment of the system exerts on it.
This generalizes the characterization of free motion in terms of a vanishing variational
derivative.
As a numerical example, the method is applied to the damped harmonic oscillator.
It is shown that the method follows accurately a change of the amplitude
by a factor of 1024 within 20 oscillation periods when taking only 32 steps for one such period.
The computed oscillation gets out of phase by an angle of 11.5 degrees
over these 20 oscillations.
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