Applied Calculus of Variations for Engineers

ISBN: 9780367378646 出版年：2018 页码：234 Komzsik, Louis CRC Press

MATHEMATICAL FOUNDATION The Foundations of Calculus of Variations The fundamental problem and lemma of calculus of variations The Legendre test The Euler-Lagrange differential equation Application: minimal path problems Open boundary variational problems Constrained Variational Problems Algebraic boundary conditions Lagrange's solution Application: iso-perimetric problems Closed-loop integrals Multivariate Functionals Functionals with several functions Variational problems in parametric form Functionals with two independent variables Application: minimal surfaces Functionals with three independent variables Higher Order Derivatives The Euler-Poisson equation The Euler-Poisson system of equations Algebraic constraints on the derivative Application: linearization of second order problems The Inverse Problem of the Calculus of Variations The variational form of Poisson's equation The variational form of eigenvalue problems Application: Sturm-Liouville problems Direct Methods of Calculus of Variations Euler's method Ritz method Galerkin's method Kantorovich's method ENGINEERING APPLICATIONS Differential Geometry The geodesic problem A system of differential equations for geodesic curves Geodesic curvature Generalization of the geodesic concept Computational Geometry Natural splines B-spline approximation B-splines with point constraints B-splines with tangent constraints Generalization to higher dimensions Analytic Mechanics Hamilton's principle for mechanical systems Elastic string vibrations The elastic membrane Bending of a beam under its own weight Computational Mechanics Three-dimensional elasticity Lagrange's equations of motion Heat conduction Fluid mechanics Computational techniques Closing Remarks References Index