NotesFAQContact Us
Search Tips
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ819227
Record Type: Journal
Publication Date: 2008-Nov
Pages: 9
Abstractor: As Provided
ISSN: ISSN-0143-0807
Brachistochrones with Loose Ends
Mertens, Stephan; Mingramm, Sebastian
European Journal of Physics, v29 n6 p1191-1199 Nov 2008
The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical mechanics, the solution of this problem is the primary example of the power of variational calculus. Here, we address the generalized brachistochrone problem that asks for the fastest sliding curve between a point and a given curve or between two given curves. The generalized problem can be solved by considering variations with varying end points. We will contrast the formal solution with a much simpler solution based on symmetry and kinematic reasoning. Our exposition should encourage teachers to include variational problems with free boundary conditions in their courses and students to try simple, intuitive solutions first. (Contains 6 figures.)
Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: Students; Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A