The simplest of the isoperimetric problems is the following:
One must set an arc with a given length from a given point of the plane to another given point such that the arc together with the line segment encloses the greatest area possible.
This task is solved in the entry example of calculus of variations.
More generally, isoperimetric problem may determining such an arc between the given points and that it gives for the integral
an extremum and that gives for another integral
a given value , as both integrals are taken along . Here, and are given functions.
The constraint (2) can be omitted by using the function instead of in (1) similarly as in the mentionned example.
|Date of creation||2013-03-22 19:12:01|
|Last modified on||2013-03-22 19:12:01|
|Last modified by||pahio (2872)|