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 |
Contents
Introduction | 1 |
Mayer formulation of variational problems | 15 |
Extremum conditions for Mayer problems | 23 |
7 other sections not shown
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Common terms and phrases
according to Eq admissible region alternative path analogous arbitrary assigned attained B₁ B₂ boat calculate Calculus of Variations catenary coefficients component arcs const containing coordinates corner conditions corner line corresponding curve denoted derivatives determined direct arc eliminating end-conditions end-coordinates end-values Euler Eqs expression extremal arc extremal field extremal path extremal stars extremum conditions extremum point Əyi f-curve fixed end-point Hence holonomic increments index value indicative point integral intersect Lagrange Lagrange problem Let us consider locus Mayer minimizing multipliers navigation problem non-derivated variables obtain ordinary minimum pieced solutions plane x,y positive prescribed problem of Sec procedure quadratic form quantity represented rope S₁ satisfied segment singular extremal slope suppose Sy₁ tangent tion tremal vanish variational problem W₁ Weierstrass device Weierstrass function write X₁ y₁ z₁ zero λ½ λ₂ ду дуг