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Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions
Version 1
: Received: 20 March 2024 / Approved: 21 March 2024 / Online: 26 March 2024 (03:02:20 CET)
A peer-reviewed article of this Preprint also exists.
Deriglazov, A.A. Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions. Universe 2024, 10, 250. Deriglazov, A.A. Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions. Universe 2024, 10, 250.
Abstract
Euler-Poisson equations 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.
Keywords
Euler-Poisson equations; exact solutions in elementary functions; constrained systems; integrable systems; spinning body in external fields
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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