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## Chapter 10CALCULUS OF VARIATIONS

When change itself can give no more’Tis easy to be true.

SIR CHARLES SEDLEY, Reasons for Constancy

### 10·01. Condition for an integral to be stationary.

Suppose that we have an integral of the form

where f is a given function; x is to be a function of t, but we have not yet specified what function. The problem of the calculus of variations is to decide what function x must be in order that S may be stationary for small variations of x. In its simplest form we can consider the determination of the shortest distance between two points. Using Cartesian coordinates and assuming that y is a differentiable function of ...

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