Brachistochrones for Repulsive Logarithmic Potential

Garry J. Tee

Abstract

Brachistochrones are constructed for repulsive central force, with logarithmic potential. Each pair of points is connected by infinitely many brachistochrones, on each of which the passage time is a local minimum, and the global minimum passage time is attained on one (or on infinitely many) of those curves. The bounded brachistochrones starting at a fixed point are separated from the unbounded brachistochrones by a Critical Brachistochrone.

Keywords

Math Review Classification

Last Updated
17/3/1999

Length
31 pages

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