Applied Calculus of Variations for Engineers, Third edition, 3rd Edition

 

Contents

Preface

Acknowledgments

Author

Introduction

IMathematical foundation

1The foundations of calculus of variations

1.1The fundamental problem and lemma of calculus of variations

1.2The Legendre test

1.3The Euler–Lagrange differential equation

1.4Minimal path problems

1.4.1Shortest curve between two points

1.4.2The brachistochrone problem

1.4.3Fermat’s principle

1.4.4Particle moving in a gravitational field

1.5Open boundary variational problems

1.6Exercises

2Constrained variational problems

2.1Algebraic boundary conditions

2.1.1Transversality condition computation

2.2Lagrange’s solution

2.3Isoperimetric problems

2.3.1Maximal area under curve with given length

2.3.2Optimal shape of curve of given length under gravity

2.4Closed-loop integrals ...