arXiv subjects

Roman V. Shamin

Publications and source records attributed to Roman V. Shamin.

3 recordsLinked to original sources

arXiv2019

The dynamics of asteroid rotation, governed by YORP effect: the kinematic ansatz

The main motivation of this research is the analytical exploration of the dynamics of asteroid rotation when it moves in elliptic orbit through Space. According to the results of Efroimsky, Frouard (2016), various perturbations (collisions, close encounters, YORP effect) destabilize the rotation of a small body (asteroid), deviating it from the initial-current spin state. This yields evolution of the spin towards rotation about maximal-inertia axis due to the process of nutation relaxation or to the proper spin state corresponding to minimal energy with a fixed angular momentum. We consider in our research the aforementioned spin state of asteroid but additionally under non-vanishing influence of the effects of non-gravitational nature (YORP effect), which is destabilizing the asteroid rotation during its motion far from giant planets. Meanwhile, new solutions for asteroid rotation dynamics in case of negligible (time-dependent) applied torques have been obtained in our development. New method for solving Euler equations for rigid body rotation is suggested; an elegant example for evolution of spin towards the rotation about maximal-inertia axis is calculated.

physics.gen-ph↗

arXiv2018

On a new type of solving procedure for Laplace tidal equation

In this paper, we present a new approach for solving Laplace tidal equations (LTE) which was formulated first in [S.V.Ershkov, A Riccati-type solution of Euler-Poisson equations of rigid body rotation over the fixed point, Acta Mechanica, 228(7), 2719 (2017)] for solving Poisson equations: a new type of the solving procedure for Euler-Poisson equations (rigid body rotation over the fixed point) is implemented here for solving momentum equation of LTE, Laplace tidal equations. Meanwhile, the system of Laplace tidal equations (including continuity equation) has been successfully explored with respect to the existence of analytical way for presentation of the solution. As the main result, the new ansatz is suggested here for solving LTE: solving momentum equation is reduced to solving system of 3 nonlinear ordinary differential equations of 1-st order in regard to 3 components of the flow velocity (depending on time t), along with the continuity equation which determines the spatial part of solution. Nevertheless, the proper elegant partial solution has been obtained due to invariant dependence between temporary components of the solution. In addition to this, it is proved here that the system of Laplace tidal equations has not the analytical presentation of solution (in quadratures) in case of nonzero fluid pressure in the Ocean, as well as nonzero total gravitational potential and the centrifugal potential (due to planetary rotation).

physics.gen-ph↗

arXiv2018

A Riccati-type solution of 3D Euler equations for incompressible flow

In fluid mechanics, a lot of authors have been reporting analytical solutions of Euler and Navier-Stokes equations. But there is an essential deficiency of non-stationary solutions indeed. In our presentation, we explore the case of non-stationary flows of the Euler equations for incompressible fluids, which should conserve the Bernoulli-function to be invariant for the aforementioned system. We use previously suggested ansatz for solving of the system of Navier-Stokes equations (which is proved to have the analytical way to present its solution in case of conserving the Bernoulli-function to be invariant for such the type of the flows). Conditions for the existence of exact solution of the aforementioned type for the Euler equations are obtained. The restrictions at choosing of the form of the 3D nonstationary solution for the given constant Bernoulli-function B are considered. We should especially note that pressure field should be calculated from the given constant Bernoulli-function B, if all the components of velocity field are obtained.

physics.flu-dyn↗