Related papers: Cartesian approach for constrained mechanical syst…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
We consider the problem of integrability of the Poisson equations describing spatial motion of a rigid body in the classical nonholonomic Suslov problem. We obtain necessary conditions for their solutions to be meromorphic and show that…
We consider Galileon models on curved spacetime, as well as the counterterms introduced to maintain the second-order nature of the field equations of these models when both the metric and the scalar are made dynamical. Working in a gauge…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action are derived. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still…
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…
We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes,…
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these syatems lead us to the…
In this work a finite element simulation of the motion of a rigid body in a fluid, with free surface, is described. A completely general referential description (of which both Lagrangian and Eulerian descriptions are special cases) of an…
A method for studying the causal structure of space-time evolution systems is presented. This method, based on a generalization of the well known Riemann problem, provides intrinsic results which can be interpreted from the geometrical…
We identify a new superintegrable Hamiltonian in 3 degrees of freedom, obtained as a reduction of pure Keplerian motion in 6 dimensions. The new Hamiltonian is a generalization of the Keplerian one, and has the familiar 1/r potential with…
The study addresses matter-coupled modified gravity, particularly $f (T, \mathcal{T})$ gravity, unveiling distinct formalism. The research further discusses stability analysis, and the dynamical system approach, exploring the dynamics of…
This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems,…
This paper showed that Poisson brackets in quaternion variables can be obtained directly from canonical Poisson brackets on cotangent bundle of $SE(3)$ (or $SO(3)$) endowed by canonical symplectic geometry. Quaternion parameters in our case…
This is the first of three papers devoted to the nonequilibrium thermodynamics of amorphous materials. Our focus here is on the role of internal degrees of freedom in determining the dynamics of such systems. For illustrative purposes, we…
We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…
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…
A stationary viscous jet falling from an oriented nozzle onto a moving surface is studied, both theoretically and experimentally. We distinguish three flow regimes and classify them by the convexity of the jet shape (concave, vertical and…
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order…