Vol. 10, No. 5, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Weak and strong solutions to the inverse-square brachistochrone problem on circular and annular domains

Christopher Grimm and John A. Gemmer

Vol. 10 (2017), No. 5, 833–856
Abstract

In this paper we study the brachistochrone problem in an inverse-square gravitational field on the unit disk. We show that the time-optimal solutions consist of either smooth strong solutions to the Euler–Lagrange equation or weak solutions formed by appropriately patched together strong solutions. This combination of weak and strong solutions completely foliates the unit disk. We also consider the problem on annular domains and show that the time-optimal paths foliate the annulus. These foliations on the annular domains converge to the foliation on the unit disk in the limit of vanishing inner radius.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/involve

We have not been able to recognize your IP address 34.232.51.240 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

Keywords
brachistochrone problem, calculus of variations of one independent variable, eikonal equation, geometric optics
Mathematical Subject Classification 2010
Primary: 49K05, 49K30, 49S05
Milestones
Received: 5 May 2016
Accepted: 24 July 2016
Published: 14 May 2017

Communicated by John Baxley
Authors
Christopher Grimm
Department of Computer Science
Brown University
Providence, RI 02912
United States
John A. Gemmer
Department of Mathematics
Wake Forest University
Winston Salem, NC 27109
United States