An identity in Calculus of Variations discovered in 1868 by Beltrami. The Euler-Lagrange Differential
Equation is

(1) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

The Beltrami identity greatly simplifies the solution for the minimal Area Surface of Revolution about a given axis between two specified points. It also allows straightforward solution of the Brachistochrone Problem.

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1999-05-26