Chaos in the Planar Two-Body Coulomb
Problem
with a Uniform Magnetic Field
Vladimir Zhdankin
Department of Physics, University of Wisconsin-Madison, Madison,
WI 53706, USA
e-mail: zhdankin@wisc.edu
J. C. Sprott
Department of Physics, University of Wisconsin-Madison, Madison,
WI 53706, USA
email: sprott@physics.wisc.edu
Abstract
The dynamics of the classical two-body Coulomb problem in a uniform
magnetic field are explored numerically in order to determine when
chaos can occur. The analysis is restricted to the configuration of
planar particles with an orthogonal magnetic field, for which there
is a four-dimensional phase space. Parameters of mass and charge are
chosen to represent physically motivated systems. To check for
chaos, the largest Lyapunov exponent and Poincar´e section are
determined for each case. We find chaotic solutions when particles
have equal signs of charge. We find cases with opposite signs of
charge to be numerically unstable, but a Poincaré section
shows that chaos occurs in at least one case.
Ref: V. Zhdankin and J. C. Sprott,
Annual Review of Chaos Theory, Bifurcations and Dynamical Systems 3, 23-33 (2013)
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