相关论文: On the Dirac Approach to Constrained Dissipative D…
Hydrodynamic turbulence is studied as a constrained system from the point of view of metafluid dynamics. We present a Lagrangian description for this new theory of turbulence inspired from the analogy with electromagnetism. Consequently it…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
We derive the Hamilton equations of motion for a constrained system in the form given by Dirac, by a limiting procedure, starting from the Lagrangean for an unconstrained system. We thereby ellucidate the role played by the primary…
Given a Dirac subbundle and an isotropic subbundle of a Courant algebroid, we provide a canonical method to obtain a new Dirac subbundle. When the original Dirac subbundle is involutive (i.e., a Dirac structure) this construction has…
In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew's triple and…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
Discrete variational methods show excellent performance in numerical simulations of mechanical systems. In this paper, we adapt discrete variational integrators for the case of mechanical systems with double-bracket dissipation. In…
Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant.…
Several new mutation-periodic quivers of period higher than 1 are introduced as well as the associated discrete dynamical systems. The reduction of these systems is developed using either a presymplectic or a Poisson approach. The…
The unified constrained dynamics is formulated without making use of the Dirac splitting of constraint classes. The strengthened, completely--closed, version of the unified constraint algebra generating equations is given. The fundamental…
The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail.
We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian…
In this work, a conformable singular system with second-class constraints is discussed. The conformable Poisson bracket (CDB) of two functions is defined. and, the Dirac theory is developed to be applicable to conformable singular systems.…
We provide a generalization of the notion of Dirac system by using Morse families to intrinsically embrace the dynamics associated with different physical systems such as constrained variational calculus, optimal control, Lagrangian…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
In this paper, we present the results of our investigation relating particle dynamics and non-commutativity of space-time by using Dirac's constraint analysis. In this study, we re-parameterise the time $t=t(\tau)$ along with $x=x(\tau)$…
This paper extends the Gotay-Nester and the Dirac theories of constrained systems in order to deal with Dirac dynamical systems in the integrable case. Integrable Dirac dynamical systems are viewed as constrained systems where the…
This paper extends the Gotay-Nester and the Dirac theories of constrained systems in order to deal with Dirac dynamical systems in the integrable case. Integrable Dirac dynamical systems are viewed as constrained systems where the…