## The Hamilton-Jacobi theory for the problems of Bolza and Mayer ... |

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### Contents

Introduction | 1 |

The multiplier rule ll | 11 |

Mayer fields for problem A | 31 |

4 other sections not shown

### Common terms and phrases

2n-parameter family admissible arc arc E1 arc for problem canonical variables Clebsch complete integral conjugate system constant continuous derivatives continuous second derivatives continuous second partial corresponding arc defined by Bliss described in Theorem determinant different from zero equations 4:8 equations 8:14 Euler-Lagrange equations extremal for problem family of extremals family of_ field as defined field for problem field theory function H functions y^(t Hamilton function Hamilton-Jacobi equation Hence homogeneous of order identically zero imbedded interior Kneser field matrix Mayer field Mayer in parametric minimizing arc multipliers neighborhood non-parametric form non-singular extremal arc normal minimizing parametric form partial differential equation points t,y problem of Bolza problem of Mayer properties described right members satisfying equations satisfying the equations second partial derivatives sense of Bliss sets of admissible Theorem 8:1 theorem follows transversal surfaces tremal y-space вдв виох^впЬв вод вчз еод их одвг рив