## Calculus of variations |

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11 pages matching **variable end-point theorem** in this book

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Very nice book to understand the topic.

### Contents

THE FUNDAMENTAL PROBLEM Introduction | 1 |

Fundamental problem | 4 |

PARAMETRIC REPRESENTATION | 5 |

Copyright | |

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### Common terms and phrases

admissible arbitrarily small arbitrary brachistochrone problem Calculus of Variations Chapter class C2 class Dt conjugate point consider constant continuous corner conditions curve joining curve of class curve T0 cycloids defined differential end-conditions end-point conditions Euler's equation Euler's rule evaluated example extremal arc extremal joining extremal of class field of extremals finite number fixed end-points geodesic Hence infimum integral of Euler's integrand isoperimetrical problem joining the end-points minimising curve minimising extremal minimum in class notation obtain one-parameter family parabola parameter parametric representation particular extremal path pencil of extremals perfect differential positive provide a weak Pt and P2 satisfied sec2 semi-field sinh slope function solid of revolution solution stationary value strong relative minimum strong variation sufficiently small surface of revolution Tt and T2 Udx+Vdy unique extremal value J0 variable end-point theorem varied curve weak relative minimum weak variation whence write x-axis xu yt zero