Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
27 (1986), S. 507-511
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The trajectory joining two points a1 and a2, which minimizes the transit time for a particle, initially at rest, to fall in a uniform gravitational field from a1 to a2, is called the brachistochrone. Johann Bernoulli was the first to find an analytical form for the brachistochrone; in 1696, he discovered that the trajectory is a cycloid. In this paper the relativistic generalization of this classic problem is presented. Four separate curves are actually identified: a particle falling in both a uniform electric and uniform gravitational field is considered. The curves that minimize the times of flight measured by an observer in a laboratory in which a1 and a2 are fixed and also the curves that minimize the proper times of flight are found.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527199
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