Jacobi's Three-Body System Moves like a Free Particle

DOI

10.2991/jnmp.2005.12.s1.40How to use a DOI?

Abstract

The problem of three bodies which attract each other with forces proportional to the cube of the inverse of their distance and move on a line was reduced to one quadrature by Jacobi [23]. Here we show that the equations of motions admit a five-dimensional Lie symmetry algebra and can be reduced to a single second-order linear equation, i.e. the equation of motion of a single free particle on the line.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - M.C. Nucci
PY  - 2005
DA  - 2005/01/01
TI  - Jacobi's Three-Body System Moves like a Free Particle
JO  - Journal of Nonlinear Mathematical Physics
SP  - 499
EP  - 506
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.40
DO  - 10.2991/jnmp.2005.12.s1.40
ID  - Nucci2005
ER  -