Coulomb dynamics near equilibrium of two equal negative charges in the field of two fixed identical positive charges

DOI10.1007/s11253-017-1307-9zbMath1447.70009OpenAlexW2603503739MaRDI QIDQ1729558

Wolodymyr Skrypnik

Publication date: 27 February 2019

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-017-1307-9

zbMATH Keywords

periodic solutionsquasiperiodic solutionsCoulomb equation of motiontwo equal negative charges

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Two-body problems (70F05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Motion of charged particles (78A35)

Related Items (7)

Coulomb planar periodic motion of \(n\) equal charges in the field of \(n\) equal positive charges fixed at a line and constant magnetic field ⋮ Periodic Coulomb dynamics of three identical negative charges in the field of four fixed identical positive charges ⋮ Periodic Coulomb dynamics of three identical negative charges in the field of six identical positive charges fixed at the vertices of octahedron ⋮ Coulomb dynamics of three equal negative charges in field of fixed two equal positive charges ⋮ Periodic Coulomb dynamics of two identical negative charges in the field of four identical fixed positive charges ⋮ Periodic Coulomb dynamics of two identical negative charges in the field of six fixed identical positive charges ⋮ Periodic Coulomb dynamics of three equal negative charges in the field of equal positive charges fixed in octagon vertices

Cites Work

• 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
• Normal modes for nonlinear Hamiltonian systems
• On the generalization of a theorem of A. Liapounoff
• Periodic orbits near an equilibrium and a theorem by Alan Weinstein
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