Junji Yamada
Publications:
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Shibayama M., Yamada J.
Nonintegrability of the Reduced Planar Three-body Problem with Generalized Force
2021, vol. 26, no. 4, pp. 439-455
Abstract
We consider the planar three-body problem with generalized potentials. Some
nonintegrability results for these systems have been obtained by analyzing the variational
equations along homothetic solutions. But we cannot apply it to several exceptional cases. For
example, in the case of inverse-square potentials, the variational equations along homothetic
solutions are solvable. We obtain sufficient conditions for nonintegrability for these exceptional
cases by focusing on some particular solutions that are different from homothetic solutions.
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