Rotation matrix of a charged symmetrical body: one-parameter family of solutions in elementary functions

Alexei A. Deriglazov

doi:10.3390/universe10060250

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arXiv · 2403.12089

Rotation matrix of a charged symmetrical body: one-parameter family of solutions in elementary functions

Alexei A. Deriglazov

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Abstract

Equations of motion of a charged symmetrical body in external constant and homogeneous electric and magnetic fields are deduced starting from the variational problem, where the body is considered as a system of charged point particles subject to holonomic constraints. The final equations are written for the center-of mass-coordinate, rotation matrix and angular velocity. General solution to the equations of motion is obtained for the case of a charged ball. For the case of a symmetrical charged body (solenoid), the task of obtaining the general solution is reduced to the problem of a one-dimensional cubic pseudo-oscillator. Besides, we present a one-parametric family of solutions to the problem in elementary functions.

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Alexei A. Deriglazov. 2024-03-12. Rotation matrix of a charged symmetrical body: one-parameter family of solutions in elementary functions. https://doi.org/10.3390/universe10060250

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