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The Variational Principles of Mechanics Book 2018 Best Study Materials

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Candidates can get Best The Variational Principles of Mechanics Books 2018 also a Top List of Main Study Materials for 2017-2018 entrance exam in India.

  • The Variational Principles of Mechanics (Dover Books on Physics)
    by Cornelius Lanczos

Syllabus

Week

Topics

1.

  • Classification of optimization problems and the place of Calculus of Variations in it.
  • Genesis of Calculus of Variations
  • Formulation of Calculus of Variations problems in geometry and mechanics

2.

  • Unconstrained minimization in n variables
  • Constrained minimization: KKT conditions
  • Sufficient conditions for constrained minimization

3.

  • Mathematical preliminaries: function, functional, metrics and metric space, norm and vector spaces
  • Banach space, Cauchy sequence; function spaces, Inner product spaces; inner product; Hilbert space; Sobolev and Lebesgue norms; continuous and linear functionals.
  • First variation of a functional; Gâteaux variation; Frechét differential; and variational derivative

4.

  • Fundamental lemma of calculus of variations and Euler-Lagrange equations

5.

  • Extension of Euler-Lagrange equations to multiple derivatives and multiple functions in a functional.
  • Calculus of variations in functionals involving two and three independent variables.

6.

  • Variational (energy) methods in statics; principles of minimum potential energy and virtual work
  • Global constraints in calculus of variations.
    Local (finite subsidiary) constrains in calculus of variations.

7.

  • General variation of a functional; transversality conditions. Broken extremals; Wierstrass-Erdmann corner conditions
  • Variational methods in dynamics: Hamilton’s principle; D’Lambert principle
  • Invariants of Euler-Lagrange equations and canonical forms; Noether’s theorem
  • Minimum characterization of Sturm-Liouville problems; Rayleigh quotient for natural frequencies and mode shapes of elastic systems

8.

  • Stability analysis and buckling using calculus of variations
  • Formulating the extremization problem starting from the differential equation; self-adjointness of the differential operator; and methods to deal with conservative and dissipative system

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