Brachistochrones for inverse square repulsion are expressed in terms of elliptic integrals, as for inverse square attraction. But, the set of brachistochrones is much more complicated than for inverse square attraction. 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, which is expressed in terms of elementary functions. |
Keywords
brachistochrone, quickest descent, constrained motion, central forces, inverse square gravity, elliptic integrals
Math Review Classification
Primary 70D05 49J15
; Secondary 01A45 49-03 70-03
Last Updated
1999-1-5
Length
34 pages
Availability
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