Two-dimensional Coulomb dynamics of two and three equal negative charges in the field of two equal fixed positive charges. (English. Ukrainian original) Zbl 1447.70011
Ukr. Math. J. 68, No. 11, 1767-1781 (2017); translation from Ukr. Mat. Zh. 68, No. 11, 1528-1539 (2016).
Summary: We find periodic and bounded (for positive time) solutions of the planar Coulomb equations of motion for two and three identical negative charges in the field of two equal fixed positive charges. The analyzed systems have equilibrium configurations and the constructed bounded solutions converge to these configurations in the infinite-time limit. The periodic solutions are obtained with the help of the Lyapunov center theorem.
MSC:
| 70F07 | Three-body problems |
| 70H12 | Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics |
| 34C25 | Periodic solutions to ordinary differential equations |
| 37C27 | Periodic orbits of vector fields and flows |
| 78A35 | Motion of charged particles |
Keywords:
periodic and bounded solutions; planar Coulomb equations of motion; equilibrium configurations; Lyapunov center theoremReferences:
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