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The Euler-Lagrange equation is a fundamental equation of the **calculus** of variations that is used to determine if a function has a stationary value. In physical terms a stationary value corresponds to a minimum or maximum of a function. The Euler-Lagrange equation is usually written as: *(∂f/∂y) - (d/dt)(∂f/∂ &ydot;) = 0*. One of the fundamental **equations** of calculus of variations states that for a function *P* defined by an integral of the form *P = f(x,y, &ydot;)dx*, where *&ydot; = dy/dt*, there is a stationary value if the corresponding Euler-Lagrange equation for that function is satisfied. When the time derivative notation is replaced by **space** **variable** notation often times, in physical problems, the partial derivative of *f* with respect to *x* is equal to 0. When this is the case the Euler-Lagrange equation is reduced to a simplified form...

This section contains 483 words(approx. 2 pages at 300 words per page) |