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Trade-offs

The brachistochrone problem is classical example used to illustrate the use of calculus of variations. In some ways it illustrates the trade-off between shortest distance (straight line) and greatest speed for a time minimization problem. The solution curve is a cycloid. In addition to the time minimization, no matter where start on the curve you will reach the end point in the same time.

brachistochrone

tautochrone

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Categories: Mathematica, Mathematics
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