40 citations · 445 across the 29 of their papers we have counts for
29 papers
Revisiting the dynamics of finite-sized satellite near the planet in ER3BP
Sergey Ershkov, Dmytro Leshchenko, Alla Rachinskaya
A novel approach for solving equations of motion of finite-sized satellite supposed to be moving in a proximity and around the planet in the elliptic restricted three-body problem,…
On the motion of satellite around the natural moons of planets using the concept of ER3BP with variable eccentricity
Sergey Ershkov, Dmytro Leshchenko, Evgeniy Prosviryakov
In the current study, we explore stability of motion of satellite around the natural moons of planets in Solar system using the novel concept of ER3BP with variable eccentricity. T…
Analysis of the size of Solar system close to the state with zero total angular momentum via Sundman inequality
Sergey Ershkov, Dmytro Leshchenko
In this paper, we present a new mathematical approach or solving procedure for analysis of the Sundman inequality (for estimating the moment of inertia of the Solar system configur…
Phoenix-Chess strategy or revisiting the algorithm for playing in Chess with incomplete information
Sergey Ershkov, Millana Ershkova
We present here the new insight or revisiting the algorithm for playing in Chess with incomplete information (which can be recognized by its newly short-name as Phoenix-Chess strat…
A new solving procedure for the Kelvin&Kirchhoff equations in case of falling a rotating torus
Sergey Ershkov, Dmytro Leshchenko, Ayrat Giniyatullin
We present in this communication a new solving procedure for Kelvin&Kirchhoff equations, considering the dynamics of falling the rigid rotating torus in an ideal incompressible flu…
Sitnikov-type solution for the motion of infinitesimal mass in BiER4BP
Sergey Ershkov, Alla Rachinskaya
In this paper, we present a new ansatz for approximated solving equations of motion of the infinitesimal mass m in case of bi-elliptic restricted problem of four bodies (BiER4BP) (…
Semi-analytical solution for the trapped orbits of satellite near the planet in ER3BP
Sergey Ershkov, Alla Rachinskaya
In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving…
On the analytical solution in non-inertial frame of R2BP
Sergey Ershkov, Dmytro Leshchenko
In this analytical study, we have presented a new type of solving procedure with aim to obtain the coordinates of small mass m, which moves around primary M_Sun, referred to non-in…
On the dynamics of non-rigid asteroid rotation
Sergey V. Ershkov, Dmytro Leshchenko
We have presented in this communication a new solving procedure for the dynamics of non-rigid asteroid rotation, considering the final spin state of rotation for a small celestial…
On a new type of solving procedure for Laplace tidal equation
Sergey V. Ershkov, Roman V. Shamin
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…
On a new type of non-stationary helical flows for incompressible couple stress fluid
Sergey V. Ershkov, Evgeniy Yu. Prosviryakov, Mikhail A. Artemov +1
We have explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space…
The dynamics of asteroid rotation, governed by YORP effect: the kinematic ansatz
Sergey V. Ershkov, Roman V. Shamin
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 E…
A Riccati-type solution of 3D Euler equations for incompressible flow
Sergey V. Ershkov, Roman V. Shamin
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…
Revolving scheme for solving a cascade of Abel equations in dynamics of planar satellite rotation
Sergey V. Ershkov
The main objective for this research was the analytical exploration of the dynamics of planar satellite rotation during the motion of an elliptical orbit around a planet. First, we…
Forbidden zones for circular regular orbits of the Moons in Solar system, R3BP
Sergey V. Ershkov
Previously, we have considered the equations of motion of the three-body problem in a Lagrange form (which means a consideration of relative motions of 3-bodies in regard to each o…
About influence of differential rotation in convection zone of gaseous or fluid giant Planet (Uranus) onto the parameters of orbits of satellites
Sergey V. Ershkov, Dmytro Leshchenko, Elbaz I. Abouelmagd
Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. We suggest in the current re…
On the invariant motions of rigid body rotation over the fixed point, via Euler angles
Sergey V. Ershkov
The generalized Euler case (rigid body rotation over the fixed point) is discussed here: - the center of masses of non-symmetric rigid body is assumed to be located at the equatori…
About existence of stationary points for the Arnold-Beltrami-Childress (ABC) flow
Sergey V. Ershkov
The existence of stationary points for the dynamical system of ABC-flow is considered. The ABC-flow, a three-parameter velocity field that provides a simple stationary solution of…
A procedure for the construction of non-stationary Riccati-type flows for incompressible 3D Navier-Stokes equations
Sergey V. Ershkov
In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations, even for 3D case of compressible gas flow o…
Dynamics of a small planetoid in Newtonian gravity field of Lagrangian configuration of three primaries
Sergey V. Ershkov, Dmytro Leshchenko, Alla Rachinskaya
Novel method for semi-analytical solving of equations of a trapped dynamics for a planetoid m4 close to the plane of mutual motion of main bodies around each other (in case of a sp…
Quasi-periodic non-stationary solutions of 3D Euler equations for incompressible flow
Sergey V. Ershkov
A novel derivation of non-stationary solutions of 3D Euler equations for incompressible inviscid flow is considered here. Such a solution is the product of 2 separated parts: - one…
Yarkovsky effect in Generalized Photogravitational 3-Bodies Problem
Sergey V. Ershkov
Here is presented a generalization of photogravitational restricted 3-bodies problem to the case of influence of Yarkovsky effect, which is known as reason of additional infinitesi…
Revisiting Apophis 2029 approach to Earth (staying on shoulders of NASA experts) or Can we be sure in almost ricocheting fly-by of Apophis on 13 of April 2029 near the Earth?
Sergey Ershkov, Dmytro Leshchenko
The main idea of this challenging research is to revisit the solar-centric dynamics of Earth around the Sun in analysis of its position on 13 April 2029 close to asteroid Apophis w…
Exact solution of Helmholtz equation for the case of non-paraxial Gaussian beams
Sergey V. Ershkov
A new type of exact solutions of the full 3 dimensional spatial Helmholtz equation for the case of non-paraxial Gaussian beams is presented here. We consider appropriate representa…