Application of Hamilton equations to Dynamic Systems

Abstract

In this presentation, instead of the Lagrangian formulation of the dynamics, we will apply the Hamiltonian formulation to be able to model and control system swidely used in applications in robotics. In the first part, we will see that using a Legendre transformation, we can associate with Lagrange's equations, which second-order equations, a system of first-order differential equations called canonical equations of Hamilton. To validate Hamilton's efficiency of formalization, the case of a manipulator with flexible joints was treated.