The answer provided at the end of the book states that: I now cite the instructions and answer as found on the book.ĭetermine the equation of the curve giving the shortest distance between two points on the surface of a cone parameterized as: As a motivating example, let us consider the problem of finding the shortest. The calculus of variations gives us precise analytical techniques to find the shortest path (i.e. This problem is a generalization of the problem of finding extrema of functions of several variables. I am interested in the development of this problem which should be done by calculus of variations. We will now generalise this to functionals. The calculus of variations is also concerned with solving extremes, but at a different level: what function should you pick to have the maximum or minimum. The calculus of variation is concerned with the problem of extrmising functional. The answer is plainly provided at the end of the book without any hint or detail and my calculations lead nowhere near the answer, so help would be appreciated. It is about a geodesic on the surface of a cone. The aim of this chapter is to give a glimpse of the main principle of the calculus of variations which, in its most basic problem, concerns minimizing. I have been trying to solve an exercice I found on a book.
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