canonical equations of motion

canonical equations of motion

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McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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The approximated integrations of the elliptical restricted three-body problem by means of perturbation technique based on Lie series and development, which led to an approximated solution of the differential system of canonical equations of motion derived from the chosen Hamiltonian function, have been discussed [25].
The particle orbits are calculated by solving the canonical equations of motion and the radiation in time and frequency domain is computed based on this data.
The canonical equations of motion are [dq.sub.i]/dt = [partial derivative]H/[partial derivative][p.sub.i] and [dp.sub.i]/dt = -[partial derivative]H/[partial derivative][q.sub.i] where ff is the Hamiltonian and under perturbations of the [[alpha].sub.i], [[beta].sub.i] one writes [[xi].sub.i] = [delta][q.sub.i] = [q.sub.i] - [q.sub.i](t) and [[eta].sub.i] = [delta][p.sub.i] = [p.sub.i] - [p.sub.i] (t) and derives equations of first approximation
Applying the canonical equations of motion, the following conservation equations follow:
Applying the canonical equations of motion to its associated Hamiltonian gives conservation equations of energy, total angular momentum and the z component of the angular momentum.