Version 1
: Received: 20 March 2024 / Approved: 21 March 2024 / Online: 26 March 2024 (03:02:20 CET)
How to cite:
Deriglazov, A.A. Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions. Preprints2024, 2024031313. https://doi.org/10.20944/preprints202403.1313.v1
Deriglazov, A.A. Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions. Preprints 2024, 2024031313. https://doi.org/10.20944/preprints202403.1313.v1
Deriglazov, A.A. Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions. Preprints2024, 2024031313. https://doi.org/10.20944/preprints202403.1313.v1
APA Style
Deriglazov, A.A. (2024). Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions. Preprints. https://doi.org/10.20944/preprints202403.1313.v1
Chicago/Turabian Style
Deriglazov, A.A. 2024 "Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions" Preprints. https://doi.org/10.20944/preprints202403.1313.v1
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.
