## Calculus of Variations: With Supplementary Notes and Exercises, 1945-1946 |

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### Contents

Hamilton Jaoobi Theory Sufficient Conditions | 54 |

The Homogeneous Case Geodesics | 76 |

Supplementary Notes to Chapter II | 90 |

6 other sections not shown

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### Common terms and phrases

admissible functions arbitrary arc length assume boundary condition boundary value problem calculus of variations canonical transformation circle arc closed conjugate point consider constant continuous function converges coordinate system corresponding defined denoted depend distance domain dxdy eigenvalue equa Euler equation Euler expression example exists extremal integral extremum family of extremals field finite number fixed follows func geodesics given gradient greatest lower bound Hamilton Hamilton-Jacobi equation Hamiltonian system harmonic function Hence implies independent variables inequality inner product integrand invariant Jacobian lattice points Legendre linear matrix method minimizing sequence minimum problem necessary condition neighborhood notation nuous obtain parameter family partial derivatives partial differential equation piecewise continuous plane polar coordinates polygonal path prescribed proof prove respect satisfying the side shortest side condition solution solved space straight line segment surface tangent theory tion transversality uniformly vanish variational problem vector zero