For functionals that do not depend explicitly on the independent variable, this equation simplifies to the Beltrami identity.
Solutions to this equation have a corner if they meet the Weierstrass-Erdmann condition. For a disk sliding on a polymer brush, the coefficient of friction can be determined by solving the fractional form of this equation. For functionals that do not depend explicitly on the independent variable, this equation simplifies to the Beltrami identity. Solving this equation proves that the minimal (*) surface for a soap film held at its ends by two wire rings is a catenoid. Finding a path for which the action is stationary is equivalent to solving this equation. The shape of the curve for which a bead accelerated from rest reaches the ground in the least time is determined by solving this equation for the brachistochrone problem. For 10 points, identify this equation central to the calculus of variations, named for two mathematicians.
Solutions to this equation have a corner if they meet the Weierstrass-Erdmann condition.
Euler-Lagrange equation