Brachistochrones for Repulsive Inverse Square Force

Garry J. Tee


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.

brachistochrone, quickest descent, constrained motion, central forces, inverse square gravity, elliptic integrals

Math Review Classification
Primary 70D05 49J15 ; Secondary 01A45 49-03 70-03

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34 pages

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