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The Darboux Inverse Problem In The Calculus Of Variations, Frank O. Lane
The Darboux Inverse Problem In The Calculus Of Variations, Frank O. Lane
Mathematics & Statistics ETDs
The simplest non-parametric problem of the calculus of variation, the so-called direct problem of the plane, is the problem of finding that arc Co of a family of admissible arcs y=y (x) joining two fixed pointed (x1 , y1 ), (x1, y2) in the x,y-plane such that along the Co the integral takes on a minimum value.