On regular polygon solutions of Coulomb equation of motion of n + 2 charges n of which are planar

DOI10.1063/1.4947421zbMath1342.78020OpenAlexW2345150294MaRDI QIDQ2804978

Wolodymyr Skrypnik

Publication date: 9 May 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4947421

zbMATH Keywords

equilibrium configurationLyapunov theoremKeplerian orbitsCoulomb equation of motion

Mathematics Subject Classification ID

Motion of charged particles (78A35)

Related Items (5)

Coulomb planar periodic motion of \(n\) equal charges in the field of \(n\) equal positive charges fixed at a line and constant magnetic field ⋮ Quasi-exact Coulomb dynamics of \(n+1\) charges \(n-1\) of which are equal ⋮ Equilibrium, regular polygons, and Coulomb-type dynamics in different dimensions ⋮ Quasi-exact Coulomb dynamics of \(n\) charges \(n\,-1\) of which are equal ⋮ Exact and quasi-exact Newton dynamics of \(n - 1\) and \(n\) bodies \(n - 1\) of which have equal masses

Cites Work

• On the holomorphic solutions of Hamiltonian equations of motion of point charges
• On exact solutions of Coulomb equation of motion of planar charges
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Periodic and bounded solutions of the Coulomb equation of motion of two and three point charges with equilibrium in the line
• On holomorphic solutions of the Darwin equations of motion of point charges
• On the generalization of a theorem of A. Liapounoff
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