The Hamiltonian Formulation of Higher Order Dynamical Systems
نویسنده
چکیده
Using Dirac’s approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the present analysis yields in a transparent manner the local structure of the associated phase space and its local sympletic geometry, and is of direct application to constrained higher order Lagrangian systems which are beyond the scope of Ostrogradsky’s approach.
منابع مشابه
Port-Hamiltonian formulation of shallow water equations with coriolis force and topography∗
Port based network modeling of complex lumped parameter physical systems naturally leads to a generalized Hamiltonian formulation of its dynamics. The resulting class of open dynamical systems are called “Port-Hamiltonian systems” [12] which are defined using a Dirac structure, the Hamiltonian and dissipative elements. This formulation has been successfully extended to classes of distributed pa...
متن کاملSensitivity Analysis of Fiber-Reinforced Lamina Micro-Electro-Mechanical Switches with Nonlinear Vibration Using a Higher Order Hamiltonian Approach
In this paper, the nonlinear free vibration of fiber-reinforced lamina micro-switches is investigated, and a sensitivity analysis (SA) is given. The switches are modeled as solid rectangular beams consisting of an isotropic matrix with transversely and longitudinally isotropic reinforcements, incorporating a higher order Hamiltonian approach. An SA of the proposed micro-switch is presented by c...
متن کاملBi–Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables
We discuss from a bi-Hamiltonian point of view the Hamilton–Jacobi separability of a few dynamical systems. They are shown to admit, in their natural phase space, a quasi–bi– Hamiltonian formulation of Pfaffian type. This property allows us to straightforwardly recover a set of separation variables for the corresponding Hamilton–Jacobi equation.
متن کاملv 1 1 0 N ov 1 99 8 ON A CLASS OF DYNAMICAL SYSTEMS BOTH QUASI - BI - HAMILTONIAN AND BI - HAMILTONIAN
It is shown that a class of dynamical systems (encompassing the one recently considered by F. Calogero in [1]) is both quasi-bi-Hamiltonian and bi-Hamiltonian. The first formulation entails the separability of these systems; the second one is obtained trough a non canonical map whose form is directly suggested by the associated Nijenhuis tensor.
متن کاملHamiltonian Approach to Poisson Lie T-Duality
The Hamiltonian formalism offers a natural framework for discussing the notion of Poisson Lie T-duality. This is because the duality is inherent in the Poisson structures alone and exists regardless of the choice of Hamiltonian. Thus one can pose alternative dynamical systems possessing nonabelian T-duality. As an example, we find a dual Hamiltonian formulation of the O(3) nonlinear σ-model. In...
متن کامل