Motion Caused by Magnetic Field in Lobachevsky Space
Abstract
We study motion of a relativistic particle in the 3-dimensional Lobachevsky space in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in the Euclidean space. Three integrals of motion are found and equations of motion are solved exactly in the special cylindrical coordinates. Motion on surface of the cylinder of constant radius is considered in detail.
- Publication:
-
The Sun, the Stars, the Universe and General Relativity: International Conference in Honor of Ya.B. Zeldovich's 95th Anniversary
- Pub Date:
- March 2010
- DOI:
- 10.1063/1.3382314
- arXiv:
- arXiv:1006.5202
- Bibcode:
- 2010AIPC.1205..108K
- Keywords:
-
- Lagrangian field theory;
- magnetic fields;
- integral equations;
- angular velocity;
- 04.20.Fy;
- 07.55.Ge;
- 02.30.Rz;
- 06.30.Gv;
- Canonical formalism Lagrangians and variational principles;
- Magnetometers for magnetic field measurements;
- Integral equations;
- Velocity acceleration and rotation;
- Mathematical Physics;
- 70;
- J.2
- E-Print:
- 4 pages