Higher order constrained Hamiltonian systems

SERGIO GRILLO

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Año: 2009 p. 82901 - 82934

0022-2488

In this paper we study a Hamiltonian formulation of the higher order constrained systems (HOCS), defined previously in Lagrangian terms. We shall focus on second order constraints in positions, i.e. second order HOCSs, which correspond, on the Hamiltonian side, to first order constraints in momenta. We show that, for affine second order constraints, existence and uniqueness conditions can be stated for their corresponding equations of motion, and that the latter can be written in terms of a Leibniz bracket. We also show that Hamiltonian systems with external forces can be described as suitable affine second order HOCSs. We study some examples, as systems with friction, and we present an application for the global asymptotic stabilization of servomechanisms.