Hamiltonian and Port-Hamiltonian Mechanics as A Possible Alternative for Helicopter Flight Dynamics Representation

Abstract

In the case of complicated, non-linear problems where simulations in the time-domain are needed to understand systems' behavior, Hamiltonian formulation can be used to obtain insight into system evolution in time. Hamiltonian dynamics has two advantages: 1) there is no need to write down the complete equations of motion explicity and thus help to solve the problem much quicker and 2) it can help understanding and designing controllers using the energy flow, Hamiltonian phase space and port-Hamiltonian representation for system evolution. The present paper highlights the importance of using the Hamiltonian dynamics for helicopter flight dynamics, exemplifying it for the helicopter pitch motion and for a 6-DOF nonlinear model. The paper shows that, using Hamiltonian formulation, one can define energy stagnations areas in the Hamiltonian phase plane and dissipative non-passive terms in the equations of motion that need to be restrained when designing a helicopter controller. The extension of the Hamiltonian to the port-Hamiltonian formulation can be used to design nonlinear controllers robust to system nonlinearities.