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A “constant of the motion” for the geodesic deviation equation

Published online by Cambridge University Press:  17 February 2009

P. Dolan ,
P. Choudhury  and
J. L. Safko
P. Dolan
Affiliation:
Department of Mathematics, Imperial College of Science and Technology, 180 Queen's Gate, London SW7 2BZ, U.K.
P. Choudhury
Affiliation:
Department of Physics, University of South Carolina, ColumbiaSouth Carolina 29200U.S.A.
J. L. Safko
Affiliation:
Department of Physics, University of South Carolina, ColumbiaSouth Carolina 29200U.S.A.
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Abstract

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In this short paper, it is shown that the geodesic deviation equation admits a “constant of the motion” and so can be solved exactly. We also derive an expression for the energy E of relative motion between two freely falling test particles. We can infer that, in general, E will not be a linear superposition of kinetic and potential energies.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 1 , July 1980 , pp. 28 - 33
Copyright
Copyright © Australian Mathematical Society 1980

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