Solvable and/or Integrable and/or Linearizable N-Body Problems in Ordinary (Three-Dimensional) Space. I

DOI

10.2991/jnmp.2000.7.3.5How to use a DOI?

Abstract

Several N -body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion ("acceleration equal force;" in most cases, the forces are velocity-dependent) and are amenable to exact treatment ("solable" and/or "integrable" and/or "linearizable"). These equations of motion are aways rotation-invariant, and sometimes translation-invariant as well. In many cases they are Hamiltonian, but the discussion of this aspect is postponed to a subsequent paper. We consider "few-body problems" (with, say, N =1,2,3,4,6,8,12,16,...) as well as "many-body problems" (N an arbitrary positive integer). The main focus of this paper is on various techniques to uncover such N -body problems. We do not discuss the detailed behavior of the solutions of all these problems, but we do identify several models whose motions are completely periodic or multiply periodic, and we exhibit in rather explicit form the solutions in some cases.

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. Bruschi
AU  - F. Calogero
PY  - 2000
DA  - 2000/08/01
TI  - Solvable and/or Integrable and/or Linearizable N-Body Problems in Ordinary (Three-Dimensional) Space. I
JO  - Journal of Nonlinear Mathematical Physics
SP  - 303
EP  - 386
VL  - 7
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2000.7.3.5
DO  - 10.2991/jnmp.2000.7.3.5
ID  - Bruschi2000
ER  -