Udwadia–Kalaba equation | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-25

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Udwadia%E2%80%93Kalaba_equation


00:00:34 1 Background
00:03:18 2 The central problem of constrained motion
00:05:54 2.1 Constraints
00:08:47 3 Equation of motion
00:18:19 4 Non-ideal constraints
00:21:40 5 Examples
00:21:49 5.1 Inverse Kepler problem
00:26:00 5.2 Inclined plane with friction
00:27:53 6 See also
00:32:21 7 References



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SUMMARY
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In theoretical physics, the Udwadia–Kalaba equation  is a method for deriving the equations of motion of a constrained mechanical system. The equation was first described by Firdaus E. Udwadia and Robert E. Kalaba in 1992. The approach is based on Gauss's principle. The Udwadia–Kalaba equation applies to a wide class of constraints, both holonomic constraints and nonholonomic ones, as long as they are linear with respect to the accelerations.  The equation generalizes to constraint forces that do not obey D'Alembert's principle.