相关论文: Exact solutions to Euler's equations for rigid bod…

The aim of this paper is to state and prove existence and uniqueness results for a general elliptic problem with homogeneous Neumann boundary conditions, often associated with image processing tasks like denoising. The novelty is that we…

In this paper we present a numerical scheme to simulate a moving rigid body with arbitrary shape suspended in a rarefied gas. The rarefied gas is simulated by solving the Boltzmann equation using a DSMC particle method. The motion of the…

A new class of exact solutions to the axisymmetric and stationary vacuum Einstein equations containing n arbitrary complex parameters and one arbitrary real solution of the axisymmetric three-dimensional Laplace equation is presented. The…

Three parameterizations are developed for modeling translational motion of a point mass in atmosphere flight over a central rotating body. Unlike well-known parameterizations such as spherical coordinate parameterizations, where position…

In the 2-dimensional curved 3-body problem, we prove the existence of Lagrangian and Eulerian homographic orbits, and provide their complete classification in the case of equal masses. We also show that the only non-homothetic hyperbolic…

The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…

The paper deals with an analytical study of various corrected Newtonian potentials. We offer a complete description of the corrected potentials, for the entire range of the parameters involved. These parameters can be fixed for different…

We construct stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of polytropic gaseous stars, with small constant angular velocity when the adiabatic exponent $\gamma$ belongs to…

A particular solution to the equations of motion of the Abelian Higgs model is given. The solution involves the Jacobi elliptic functions as well as the Heun functions.

In this paper we propose a new approach to the study of integrable cases based on intensive computer methods' application. We make a new investigation of Kovalevskaya and Goryachev-Chaplygin cases of Euler-Poisson equations and obtain many…

The motion of a rigid body is described in Classical Mechanics with the venerable Euler's equations which are based on the assumption that the relative distances among the constituent particles are fixed in time. Real bodies, however,…

Vortices (flows with closed elliptic streamlines) are exact nonlinear solutions to the compressible Euler equation. In this contribution, we use differential geometry to derive the transformations between Cartesian and elliptic coordinates,…

We compute explicitly the equations of motion of the Hamiltonian formulation of quadratic gravity. This is the theory with the most general Lagrangian with terms of quadratic order in the curvature tensor. We employ the symbolic…

The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently…

In this article we consider nonholonomic deformations of disk solutions in general relativity to generic off-diagonal metrics defining knew classes of exact solutions in 4D and 5D gravity. These solutions possess Lie algebroid symmetries…

We compare three approaches to posing the index 3 set of differential algebraic equations (DAEs) associated with the constrained multibody dynamics problem formulated in absolute coordinates. The first approach works directly with the…

The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…

In the present paper, an analysis was performed on the torque-free motion of a rigid body, developing Euler's analytical solution and Poinsot's geometric solution. From mathematical formulations, the analytical solution for the time…

It is attempted to obtain the masses of the celestial bodies, the initial conditions of their motion, and the constant of gravitation, by a global parameter optimization. First, a numerical solution of the N-bodies problem for mass points…

Exact solutions are studied in the context of modified Brans-Dicke theory. The non-linearity of the modified Brans-Dicke field equations is treated with the Euler-Duarte-Moreira method of integrability of anharmonic oscillator equation.…