相关论文: Singular Lagrangian Systems on Jet Bundles
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
We rederive the results of our companion paper, for matching spacetime and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the Palatini action contains second class…
The recently modified Faddeev-Jackiw formalism for systems having one chain of four levels of only second-class constraints is applied to the non-trivial a=1 bosonized chiral Schwinger model in (1+1) dimensions as well as to one mechanical…
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…
New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics…
It is shown that an arbitrary singular Lagrangian theory (with first and second class constraints up to $N$-th stage in the Hamiltonian formulation) can be reformulated as a theory with at most third-stage constraints. The corresponding…
In this paper we explore the idea of looking at the Dirac quantisation conditions as $\hbar$-dependent constraints on the tangent bundle to phase-space. Starting from the path-integral version of classical mechanics and using the natural…
Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the…
This paper presents a geometric description on Lie algebroids of Lagrangian systems subject to nonholonomic constraints. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the…
In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. Starting with the Covariant Force Law, we first develop autonomous…
A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…
We study geometry of the phase space for finite-dimensional dynamical systems with degenerate Lagrangians. The Lagrangian and Hamiltonian constraint formalisms are treated as different local-coordinate pictures of the same invariant…
A comparative analysis of two different versions of the Legendre transformation is presented. We provide an almost complete although somewhat superficial review of the geometric background for analytical mechanics. Complete coordinate…
The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the…
The aim of the paper is to study some dynamic aspects coming from a tangent form, i.e. a time dependent differential form on a tangent bundle. The action on curves of a tangent form is natural associated with that of a second order…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are…
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational…
Although conservative Hamiltonian systems with constraints can be formulated in terms of Dirac structures, a more general framework is necessary to cover also dissipative systems such as gradient and metriplectic systems with constraints.…