Related papers: On the geometry of generalized Chaplygin systems
We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…
We have developed an action formulation for the Generalized Chaplygin Gas (GCG). The most general form for the nonrelativistic GCG action is derived consistent with the equation of state. We have also discussed a relativistic formulation…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
We present general reduction procedures for Courant, Dirac and generalized complex structures, in particular when a group of symmetries is acting. We do so by taking the graded symplectic viewpoint on Courant algebroids and carrying out…
This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding…
This paper discusses reduction by symmetries for autonomous and non-autonomous forced mechanical systems with inelastic collisions. In particular, we introduce the notion of generalized hybrid momentum map and hybrid constants of the motion…
The Faddeev-Jackiw symplectic formalism for constrained systems is applied to analyze the dynamical content of a model describing two massive relativistic particles with interaction, which can also be interpreted as a bigravity model in one…
In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees of freedom. As special cases we extract…
In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…
We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
Generalized parameter estimation-based observers have proven very successful to deal with systems described in state-affine form. In this paper, we enlarge the domain of applicability of this method proposing an algebraic procedure to…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the…
For Hamiltonian field theories on polysymplectic manifolds with a symmetry group action and a momentum map, we explore the redundancy in a set of necessary conditions that has appeared in the literature, for a generalized version of the…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In…
In this paper we study the coisotropic reduction in different types of dynamics according to the geometry of the corresponding phase space. The relevance of the coisotropic reduction is motivated by the fact that these dynamics can always…
We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a…
The patch dynamics scheme in equation-free multiscale modelling can efficiently predict the macroscopic behaviours by simulating the microscale problem in a fraction of the space-time domain. The patch dynamics schemes developed so far, are…