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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according admissible alternative applications arbitrary assigned assumed attained B₁ B₂ boat branch calculate called changes Chapter component connection Consequently consider considerations constant containing coordinates corner corresponding covered curve defined denoted depend derivatives determined difference direct effects eliminating end-conditions end-points energy Euler Eqs example exists expression extremal arc extremal path extremum conditions f-curve fact field fixed forced function give given Hence hold increments indicative initial instance integral intersect introducing length limited means minimizing minimum multipliers neighboring obtain pieced plane positive prescribed present problem procedure proved quantity reached reduce region remark represented rope satisfied segment situation slope solution starting straight stream suppose tangent tion vanish variables variation Weierstrass write written y₁ y₂ yields λ₂