AMATH 456 - Calculus of Variations
David Siegel
Fall 2015
Course notes by Kirsten Morris
Introduction, Calculus, Convexity, Functionals
Variation, Convex Functionals, Euler-Lagrange Equation, Fundamental Lemma
Brachistochrone
Constraints, Special Cases of Euler-Lagrange Equations
More Brachistochrone, Free End-Point Problems, Variable End-Point Problems, Dido's Problem
Integrals with Higher Derivatives, Elastic Beam, Cantilever Beam
Vector-Valued Functions
Hamilton's Principle, Kepler's Laws, Generalized Coordinates, Canonical Equations
Optimal Control, Rocket Car, General Formulation
Pontryagin Maximum Principle, Rocket Car, Simple Harmonic Oscillator
Linear Systems, Linear Quadratic Control
Control which is not Bang-Bang