June 2014
Intermediate to advanced
233 pages
5h 42m
English
Content preview from Applied Calculus of Variations for Engineers, 2nd Edition
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Contents
Preface to the second edition xi
Preface to the first edition xiii
Acknowledgments xv
About the author xvii
List of notations xix
I Mathematical foundation 1
1 The foundations of calculus of variations 3
1.1 The fundamental problem and lemma of calculus of variations 3
1.2 TheLegendretest ........................ 7
1.3 The Euler-Lagrange differential equation . . . . . . . . . . . . 9
1.4 Application:minimalpathproblems .............. 11
1.4.1 Shortest curve between two points . . . . . . . . . . . 12
1.4.2 Thebrachistochroneproblem .............. 14
1.4.3 Fermat’sprinciple .................... 18
1.4.4 Particle moving in the gravitational field . . ...
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