Symmetry methods in collisionless many-body problems
UNSPECIFIED. (1996) Symmetry methods in collisionless many-body problems. JOURNAL OF NONLINEAR SCIENCE, 6 (6). pp. 543-563. ISSN 0938-8974Full text not available from this repository.
We formulate an appropriate symmetry context for studying periodic solutions to equal-mass many-body problems in the plane and 3-space. In a technically tractable but unphysical case (attractive force a smooth function of squared distance, bodies permitted to coincide) we apply the equivariant Moser-Weinstein Theorem of Montaldi et al. to prove the existence of various symmetry classes of solutions. In so doing we expoit the direct product structure of the symmetry group and use recent results of Dionne et al. on 'C-axial' isotropy subgroups. Along the way we obtain a classification of C-axial subgroups of the symmetric group. The paper concludes with a speculative analysis of a three-dimensional solution to the 2n-body problem found by Davies el al. and some suggestions for further work.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
Q Science > QC Physics
|Journal or Publication Title:||JOURNAL OF NONLINEAR SCIENCE|
|Number of Pages:||21|
|Page Range:||pp. 543-563|
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