Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
28 (1987), S. 705-710
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The stationary action problem for a single, classical, point particle in external gravitational and electromagnetic fields is written in optimal control format. The relativistic interval is the independent variable and time, space, and action are the five dependent variables. A general metric is used for the space-time manifold so that the equations are manifestly covariant. The form of the system equations guarantees that the particle moves with unit speed with respect to interval. The Lagrangian is a function of the metric tensor and the electromagnetic four-potential, but not of particle parameters such as electric charge q and mass m. The Hamiltonian is not identically zero, unlike those derived in many earlier analyses. A constant of the motion is found that is identified with q/mc2. An explanation is presented for the classical inequality m≥0. The trajectories can reduce to geodesics and even further to those governed by Fermat's principle of stationary time.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527826
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