Related papers: Rotating frame analysis of rigid body dynamics in …
We consider robust estimation of wrapped models to multivariate circular data that are points on the surface of a $p$-torus based on the weighted likelihood methodology.Robust model fitting is achieved by a set of weighted likelihood…
The motion of a rolling ball actuated by internal point masses that move inside the ball's frame of reference is considered. The equations of motion are derived by applying Euler-Poincar\'e's symmetry reduction method in concert with…
In many real-world settings, image observations of freely rotating 3D rigid bodies may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
We give an elementary derivation of the Montgomery phase formula for the motion of an Euler top, using only basic facts about the Euler equation and parallel transport on the 2-sphere (whose holonomy is seen to be responsible for the…
We study the motion of a compressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free…
This paper is devoted to the analysis of random motions on the line and in the space R^d (d > 1) performed at finite velocity and governed by a non-homogeneous Poisson process with rate \lambda(t). The explicit distributions p(x,t) of the…
Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for…
We develop a new geometrical technique to study relative equilibria for a system of $n$--positive masses, moving on the two dimensional sphere $\mathbb{S}^2$, under the influence of a general potential which only depends on the mutual…
This study proposes the topology optimization method for moving rigid bodies subjected to forces from fluid flow, such as sails and turbines, with an unsteady time-dependent formulation. Unlike existing topology optimization frameworks in…
In meteorology the analysis of motions of the atmosphere on the Earth has been done using various mathematical models and using various approximations. In this article as the simplest model the compressible Euler equations with barotropic…
Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is…
An algebraic procedure of getting of canonical variables in a rigid body dynamics is presented. The method is based on using a structure of an algebra of Lie-Poisson brackets with which a Hamiltonian dynamics is set. In a particular case of…
Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum…
Dynamical system methods are used in the study of the stability of spatially flat homogeneous cosmologies within a large class of generalized modified gravity models in the presence of a relativistic matter-radiation fluid. The present…
The shape of liquid surface in a rotating frame depends on the angular velocity. In this experiment, a fluid in a rectangular container with a small width is placed on a rotating table. A smartphone fixed to the rotating frame…
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…
Linearised relativistic elasticity equations of motion are considered for a rod and a spinning ring encountering a gravitational wave. In the case of the rod, the equations reduce to a wave equation with appropriate boundary conditions.…
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…
The traditional way of estimating the gravitational field from observed motions of test objects is based on the virial relation between their kinetic and potential energy. We find a more efficient method. It is based on the natural…