Singularity of Stoermer's problem

Details Singularity of Stoermer's problem Singularity of Stoermer's problem

May 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..27...39e&link_type=abstract

Celestial Mechanics, vol. 27, May 1982, p. 39-52. In French.

Mathematics

Charged Particles, Magnetic Dipoles, Particle Trajectories, Singularity (Mathematics), Hamiltonian Functions, Homogeneity, Many Body Problem

Scientific paper

A charged particle is considered to be influenced by a magnetic dipole in order to examine the effects of a singularity on a point mass and the neighborhood. Cylindrical and Cartesian coordinates are defined for normalizing the problem in terms of Lagrangian and Hamiltonian functions. The second derivative of the Viriel identity in the n-body problem is used in an examination of particle trajectories in the case of homogeneity of the field and of trajectories near or far from the singularity. The behavior of a particle near a singularity is numerically formulated on a unit sphere in spherical coordinates. The factor r is found to decrease when the particle is nearing collision, and increase when the particle is part of an expanding system. It is noted that r can never become zero.

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