Stability of equilibrium points in the three-dipole problem

Details Stability of equilibrium points in the three-dipole problem Stability of equilibrium points in the three-dipole problem

Apr 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993ap%26ss.202..289d&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 202, no. 2, p. 289-313.

Mathematics

Dynamical Systems

2

Charged Particles, Electromagnetic Fields, Magnetic Dipoles, Particle Motion, Systems Stability, Three Body Problem, Dynamical Systems, Lorentz Force, Matrices (Mathematics), Polynomials, Taylor Series

Scientific paper

In the three dipole problem we assume each one of the magnetic dipoles to be located on one member of a three celestial bodies system moving in circles according to the equilateral solution of Lagrange. Using the method of characteristic exponents we study here for the first time the stability of planar and three dimensional equilibrium points of charged particles moving under the electromagnetic force of the system. Applying this theoretical procedure we give an extensive numerical investigation for the stability of the equilibria for a lot of combinations of the values of the parameters of the electromagnetic field.

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