Abstract
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable the relativistic dynamic equation for systems with an invariant plane becomes a non-linear analytic equation in one complex variable. We obtained explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By assuming the Clock hypothesis and using these solutions, we were able to describe the space-time transformations between two uniformly accelerated and rotating systems.
Similar content being viewed by others
References
W.E. Baylis: Electrodynamics, A Modern Geometric Approach. Progress in Physics, Vol. 17, Birkhauser, Boston, 1999.
S. Takeuchi: Phys. Rev. E 66 (2002) 37402–1.
Y. Friedman and M. Semon: Phys. Rev. E 72 (2005) 026603.
Y. Friedman: Homogeneous balls and their Physical Applications, Progress in Mathematical Physics, Vol. 40, Birkhauser, Boston, 2004.
Y. Friedman and Yu. Gofman: arxiv/gr-qc/0509004.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Friedman, Y. Explicit solutions for relativistic acceleration and rotation. Czech J Phys 55, 1403–1408 (2005). https://doi.org/10.1007/s10582-006-0017-6
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10582-006-0017-6