Cover: On a Brachistochrone Problem of Victorr Erma.

On a Brachistochrone Problem of Victorr Erma.

Published 1972

by Kenneth Saunders

Purchase Print Copy

 Format Price
Add to Cart Paperback18 pages $20.00

The following variation of a classical brachistochrone is considered: the particle must start and end at the same elevation with horizontal velocities, and must never "fly-off" the curve of its own inertia. First, it is shown that the problem can be reduced to that of finding brachistochrones that start horizontally and go to a specified vertical line, the corresponding particles constrained to never "fly-off" of their own inertia. This problem is then formulated as an optimal control problem with a state-dependent inequality constraint on the control. It is then shown that, strictly speaking, the problem has no solution but that interesting local extrema can be found. Graphs of these extrema are given and the resulting times are compared with those for the corresponding classical brachistochrone. 18 pp. Ref. (Author)

This report is part of the RAND paper series. The paper was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.