Frenay – Serre equations for the trajectory of a charged particle in a magnetic dipole

Heading: 
Space and Atmospheric Physics
1Nosov, SF, 1Malovichko, PP
1Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
Kosm. nauka tehnol. 2002, 8 ;(Supplement2):046-054
https://doi.org/10.15407/knit2002.02s.046
Publication Language: Russian
Abstract: 
The methods of differential geometry consider the trajectories of charged particles in the field of a magnetic dipole. The parameters of the curvature and torsion of the trajectories of the particles and the trajectories of their leading centers are determined. One of the results of the work that can have important physical applications is the discovered effect of exceeding the mean square frequency of rotation of the Fresnay trihedron relative to the Larmor frequency. This effect is especially pronounced for particles propagating along curved magnetic field lines at a small pitch angle.
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