Related papers: Dirac Structures in Vakonomic Mechanics

We consider Hamiltonian formulation of a dynamical system forced to move on a submanifold $G_\alpha(q^A)=0$. If for some reasons we are interested in knowing the dynamics of all original variables $q^A(t)$, the most economical would be a…

Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex…

The usual treatment of a (first order) classical field theory such as electromagnetism has a little drawback: It has a primary constraint submanifold that arise from the fact that the dynamics is governed by the antisymmetric part of the…

In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of $TT^*Q$…

Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical…

This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…

We discuss the use of the variational principle within quaternionic quantum mechanics. This is non-trivial because of the non commutative nature of quaternions. We derive the Dirac Lagrangian density corresponding to the two-component Dirac…

In this paper, we present a collection of infinite-dimensional systems with nonholonomic constraints. In finite dimensions the two essentially different types of dynamics, nonholonomic or vakonomic ones, are known to be obtained by taking…

Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…

We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…

In order to obtain a framework in which both non-holonomic mechanical systems and non-holonomic mechanical systems with symmetry can be described, we introduce in this paper the notion of a Lagrangian system on a subbundle of a Lie…

Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new variational principle to uncover more insights…

Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems…

The main aim of the present paper is to raise the doubt that vakonomic dynamics may not be satisfactory as a model for velocity dependent constraints.

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.…

We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…

We propose a new description of dynamics of autonomous mechanical systems which includes the momentum-velocity relation. This description is formulated as a variational principle of virtual action more complete than the Hamilton Principle.…

A relation between variational principles for equations of continuum mechanics in Eulerian and Lagrangian descriptions is considered. It is shown that for a system of differential equations in Eulerian variables corresponding Lagrangian…

This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known…