Related papers: Generalized virial theorem for contact Hamiltonian…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
In this paper we propose a Hamilton-Jacobi theory for implicit contact Hamiltonian systems in two different ways. One is the understanding of implicit contact Hamiltonian dynamics as a Legendrian submanifold of the tangent contact space,…
In this paper we study the kinetic theory of many-particle astrophysical systems imposing axial symmetry and extending our previous analysis in Phys. Rev. D 83, 123007 (2011). Starting from a Newtonian model describing a collisionless…
The Hamiltonian constraint system is the canonical formulation of a physical system with a Hamiltonian constrained to vanish. In terms of the canonical variables, we define what we call reference observable, with respect to which other…
We investigate the particle and kinetic-energy densities for a system of $N$ fermions confined in a potential $V(\bfr)$. In an earlier paper [J. Phys. A: Math. Gen. {\bf 36}, 1111 (2003)], some exact and asymptotic relations involving the…
The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of Hamiltonian vector…
The Standard Model of particle physics was established based on the equivalence principle and gauge invariance. The Lagrangians were built upon experimental data demonstrating the violation of discrete symmetries together with ideas of…
While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a…
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…
We present a global approach of non-dissipative physics. Based on symplectic mechanics this technique allows us to obtain the solution of a very large class of problems in terms of a Taylor expand. We apply this method to the problem of…
An equation is obtained to find the Lagrangian for a one-dimensional autonomous system. The continuity of the first derivative of its constant of motion is assumed. This equation is solved for a generic nonconservative autonomous system…
A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result. The only ingredients required for the…
A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics (MHD)…
The Virial Theorem in the one- and two-dimensional spherical geometry are presented, in both classical and quantum mechanics. Choosing a special class of Hypervirial operators, the quantum Hypervirial relations in the spherical spaces are…
A generalization of Coulomb-Amontons' law of dry friction recently proposed by V. V. Kozlov is considered in the context of rigid body dynamics. Universal requirements for dry friction tensor formulated by V. V. Kozlov are complemented by a…
Integrable Hamiltonian systems on almost-symplectic manifolds have recently drawn some attention. Under suitable properties, they have a structure analogous to those of standard symplectic-Hamiltonian completely integrable systems. Here we…
In the framework of 2D ideal Hydrodynamics a vortex system is defined as a smooth vorticity function having few positive local maxima and negative local minima separated by curves of zero vorticity. Invariants of such structures are…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and…