Rotation matrix of a charged symmetrical body: one-parameter family of solutions in elementary functions
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914826613161984 |
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| author | Deriglazov, Alexei A. |
| author_facet | Deriglazov, Alexei A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rotation matrix of a charged symmetrical body: one-parameter family of solutions in elementary functions Deriglazov, Alexei A. Classical Physics Mathematical Physics Exactly Solvable and Integrable Systems 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. |
| title | Rotation matrix of a charged symmetrical body: one-parameter family of solutions in elementary functions |
| topic | Classical Physics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2403.12089 |