Mathematics

 In the classical calculus of variations one studies optimization problems on infinite-dimensional spaces. The information about the first and the second variation of the minimized functional is encoded in the solutions of some ordinary differential equations. In this talk I am going to show how these classical results can be generalized to a much wider class of optimal control problems using symplectic geometry. In particular we are going to see what are the proper generalizations of Euler-Lagrange and Jacobi equations in the case of just one independent variable.