Related papers: The generalized Euler-Poinsot rigid body equations…
Dynamical equations in generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, take a rather simple form, even though an infinite number of conserved charges are taken into account. We show…
We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in so-called "quantized spaces". Our main result is a description of the…
The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a…
We derive a simple Poisson structure in the space of Fourier modes for the vorticity formulation of the Euler equations on a three-dimensional periodic domain. This allows us to analyse the structure of the Euler equations using a…
We present an L-A pair for the Apel'rot case of a heavy rigid 3-dimensional body. Using it we give an algebro-geometric integration procedure. Generalizing this L-A pair, we obtain a new completely integrable case of the Euler-Poisson…
We study the Euler-Poincar\'e equations that are the regularized Euler equations derived from the Euler-Poincar\'e framework. It is noteworthy to remark that the Euler-Poincar\'e equations are a generalization of two well-known…
Starting from the following multidimensional integrable generalizations of the heavy rigid body systems: the Euler top, the Lagrange top, the Lagrange bitop, and the totally symmetric case, we add to each of them a gyroscope. For each of…
The covariant Poisson equation for Lie algebra-valued mappings defined in 3-dimensional Euclidean space is studied using functional analytic methods. Weighted covariant Sobolev spaces are defined and used to derive sufficient conditions for…
The Poisson structures for 3D systems possessing one constant of motion can always be constructed from the solution of a linear PDE. When two constants of the motion are available the problem reduces to a quadrature and the structure…
We give sufficient conditions for the rigid body in the presence of an axisymmetric force field and a gyroscopic torque to admit a Hamilton-Poisson formulation. Even if by adding a gyroscopic torque we initially lose one of the conserved…
This article aims to derive equations of motion for dynamical systems with angular momentum on Finsler geometries. To this end, we apply Souriau's Principle of General Covariance, which is a geometrical framework to derive diffeomorphism…
Using recent developments in the theory of globally defined expanding compressible gases, we construct a class of global-in-time solutions to the compressible 3-D Euler-Poisson system without any symmetry assumptions in both the…
We establish the procedure to derive from an action-based variational principle the classical equations of motion in Hamiltonian phase space of a particle subject to general position and velocity dependent non-holonomic equality…
Euler's equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson…
We formulate Euler-Poincar\'e and Lagrange-Poincar\'e equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial…
In our previous paper, based on the Carter & Quintana framework and the Damour-Soffel-Xu scheme, we deduced a complete and closed set of post-Newtonian dynamical equations for elastically deformable astronomical bodies. In this paper, we…
We study the long-time behavior of an elliptic rigid body which is allowed to vertically translate and rotate in a 2D unbounded channel under the action of a Poiseuille flow at large distances. The motion of the fluid is modelled by the…
Compressible Euler-Poisson equations are the standard self-gravitating models for stellar dynamics in classical astrophysics. In this article, we construct periodic solutions to the isothermal ($\gamma=1$) Euler-Poisson equations in $R^{2}$…
We give a necessary and sufficient condition for the global existence of the classical solution to the Cauchy problem of the compressible Euler-Poisson equations with radial symmetry. We introduce a new quantity which describes the balance…
The fundamental equation describing the rotational dynamics of a rigid body is ${\vec \tau}=d{\vec L} / dt$ which is a straightforward consequence of the Newton's second law of motion and is only valid in an inertial coordinate system.…