Czechoslovak Journal of Physics

, Volume 55, Issue 11, pp 1403–1408 | Cite as

Explicit solutions for relativistic acceleration and rotation

  • Yaakov Friedman


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.

Key words

relativistic dynamics accelerated systems maximal acceleration 


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  1. [1]
    W.E. Baylis: Electrodynamics, A Modern Geometric Approach. Progress in Physics, Vol. 17, Birkhauser, Boston, 1999.Google Scholar
  2. [2]
    S. Takeuchi: Phys. Rev. E 66 (2002) 37402–1.CrossRefADSGoogle Scholar
  3. [3]
    Y. Friedman and M. Semon: Phys. Rev. E 72 (2005) 026603.CrossRefADSGoogle Scholar
  4. [4]
    Y. Friedman: Homogeneous balls and their Physical Applications, Progress in Mathematical Physics, Vol. 40, Birkhauser, Boston, 2004.Google Scholar
  5. [5]
    Y. Friedman and Yu. Gofman: arxiv/gr-qc/0509004.Google Scholar

Copyright information

© Institute of Physics, Academy of Sciences of Czech Republic 2005

Authors and Affiliations

  • Yaakov Friedman
    • 1
  1. 1.Jerusalem College of TechnologyJerusalemIsrael

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