Problem of the Minimum Rotation Surface
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Description: Java applet demonstrating the catenary.
PROBLEM OF THE MINIMUM ROTATION-SURFACE It is necessary to find a generating line of the rotation-surface with minimum area. It is known that the line to be found is a catenary. Depending on the concrete boundary conditions, there can exist either two solutions of the Euler equation or alone or none. These solutions are catenaries. In traditional courses, one does not pay attention enough to the case of absence of the classic solution. In the numerical solution by the Euler method, the broken-wise solution is easily discovered. These are two disks for which the generating line consists of two vertical segments and a horizontal one lying on the axis of rotation. Moreover, the broken-wise solution can be a global minimum in the zone of existing the solution for the Euler equation (
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| Page title: | PROBLEM OF THE MINIMUM ROTATION-SURFACE |
| Keywords: | calculus of variations IAGSoft JAVA applet PROBLEM OF THE MINIMUM ROTATION-SURFACE |
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| IP-address: | 195.19.132.154 |
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| Date | created: 1997.11.01 Last updated on 2014.02.03 02:01:35 MSK |