New results for time reversed symplectic dynamic systems and quadratic functionals

Abstract

In this paper, we examine time scale symplectic (or Hamiltonian) systems and the associated quadratic functionals which contain a forward shift in the time variable. Such systems and functionals have a close connection to Jacobi systems for calculus of variations and optimal control problems on time scales. Our results, among which we consider the Reid roundabout theorem, generalize the corresponding classical theory for time reversed discrete symplectic systems, as well as they complete the recently developed theory of time scale symplectic systems.

Keywords

• time scale
• symplectic system
• linear hamiltonian system
• quadratic functional
• jacobi system
• reid roundabout theorem