Related papers: Rotating frame analysis of rigid body dynamics in …
We investigate the three-dimensional structure of the pulsar magnetosphere through time-dependent numerical simulations of a magnetic dipole that is set in rotation. We developed our own Eulerian finite difference time domain numerical…
Rotation of a permanently polarized rigid body under the radiation reaction torque is considered. Dynamics of the spinning top is derived from a balance condition of the angular momentum. It leads to the non-integrable nonlinear 2nd-order…
The purpose of this article is to compute the normal form of a class of general quadratic Hamiltonian systems that generalizes naturally Euler's equations from the free rigid body dynamics.
Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential…
We prove a priori estimates for the three-dimensional compressible Euler equations with moving {\it physical} vacuum boundary, with an equation of state given by $p(\rho) = C_\gamma \rho^\gamma $ for $\gamma >1$. The vacuum condition…
The parameterisation of rotations in three dimensional Euclidean space is an area of applied mathematics that has long been studied, dating back to the original works of Euler in the 18th century. As such, many ways of parameterising a…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
Using Euler's equations of motion and the Hamiltonian formulation, we obtain the equations of motion of systems with internal angular momentum that are moving with respect to a given reference frame, when subjected to a torque which is…
We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has…
Physical simulation-based optimization is a common task in science and engineering. Many such simulations produce image- or tensor-based outputs where the desired objective is a function of those outputs, and optimization is performed over…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…
A model of the three-dimensional rotating compressible Euler equations on the cubed sphere is presented. The model uses a mixed mimetic spectral element discretization which allows for the exact exchanges of kinetic, internal and potential…
The classical Euler--Poinsot case of the rigid body dynamics admits a class of simple but non-trivial integrable generalizations, which modify the Poisson equations describing the motion of the body in space. These generalizations possess…
In this introductory review article, we explore the special relativistic equations of particle motions and the consequent derivation of Einstein's famous formula $E=mc^2$. Next, we study the special relativistic electromagnetic field…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
Several methods of time discretization are examined for integrable rigid body models, such as Euler, Lagrange, and Kowalevski tops. Problems of Lax-Moser pairs, conservation laws, and explicit solver algorithms are discussed. New…
This paper presents a method of computing free motions of a planar assembly of rigid bodies connected by loose joints. Joints are modeled using local distance constraints, which are then linearized with respect to configuration space…
We discuss global tensor invariants of a rigid body motion in the cases of Euler, Lagrange and Kovalevskaya. These invariants are obtained by substituting tensor fields with cubic on variable components into the invariance equation and…