Junji Yamada


Shibayama M., Yamada J.
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.
Keywords: nonintegrability, three-body problem
Citation: Shibayama M., Yamada J.,  Nonintegrability of the Reduced Planar Three-body Problem with Generalized Force, Regular and Chaotic Dynamics, 2021, vol. 26, no. 4, pp. 439-455

Back to the list