The symplectic character of periodic orbits in the three dipole problem

Details The symplectic character of periodic orbits in the three dipole problem The symplectic character of periodic orbits in the three dipole problem

Oct 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994ap%26ss.220..167k&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 220, no. 2, p. 167-178

Mathematics

2

Asymmetry, Charged Particles, Dipoles, Electromagnetic Fields, Mathematical Models, Numerical Integration, Orbits, Equations Of Motion, Hamiltonian Functions, Matrices (Mathematics), Vectors (Mathematics)

Scientific paper

In this work we reveal for the first time that in the three dipole problem only asymmetric periodic orbits exist. For these periodic orbits -- planar and three dimensional -- of a charged particle moving under the influence of the electromagnetic field of the three dipoles we give their symplectic relations using the Hamiltonian formulation which is related to the symplectic matrix. Also we study the properties of the symplectic matrix and we give the relations there are among the variations of a periodic solution. These relations have been used to check the accuracy of numerical integration of equations of first order variations.

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