## An engineering approach to the calculus of variations: the techniques for the solution of variational problems in Mayer form, presented at Purdue University, USA, engineering sciences and aeronautical engineering seminars, October-December, 1956 |

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### Contents

Introduction Pago | 1 |

Chapter 1 Extremum conditions for ordinary minimus problems | 4 |

Mayer formulation of variational problems | 15 |

13 other sections not shown

### Common terms and phrases

abscissa according to Eq admissible region alternative path analogous arbitrary arc A-Z attained boat calculate Calculus of Variations catenary center of curvature coefficients component arcs configuration const containing coordinates corner conditions corner line corresponding defined definite integral denoted dependent variables derivatives determined deviation direct arc eliminating end-coordinates end-values Euler Eqs example expression extremal arc extremal field extremal path extremal solution extremal stars extremum conditions extremum point fixed end-point problem Hence increments index value indicative point integral intersect Lagrange problem Let us consider locus means of Eq minimizing g multipliers navigation problem neighboring extremal non-derivated variables obtain ordinary minimum parameters pieced solutions plane x,y positive prescribed problem of Sec procedure Prom Purthermore quadratic form reflexed represented rope segment singular extremal situation slope suppose tangent tion tremal vanish variable end-points variational problem Weierstrass condition Weierstrass device Weierstrass function write F written yields zero