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2013
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# Sergey Ramodanov

Universitetskaya 1, Izhevsk, 426034 Russia
Institute of Computer Science, Udmurt State University

Senior scientist, Department of Mathematical Methods in Nonlinear Dynamics, IMM UB RAS

## Publications:

 Ramodanov S. M., Sokolov S. V. Dynamics of a Circular Cylinder and Two Point Vortices in a Perfect Fluid 2021, vol. 26, no. 6, pp.  675-691 Abstract We study a mechanical system that consists of a 2D rigid body interacting dynamically with two point vortices in an unbounded volume of an incompressible, otherwise vortex-free, perfect fluid. The system has four degrees of freedom. The governing equations can be written in Hamiltonian form, are invariant under the action of the group $E$(2) and thus, in addition to the Hamiltonian function, admit three integrals of motion. Under certain restrictions imposed on the system’s parameters these integrals are in involution, thus rendering the system integrable (its order can be reduced by three degrees of freedom) and allowing for an analytical analysis of the dynamics. Keywords: point vortices, Hamiltonian systems, reduction Citation: Ramodanov S. M., Sokolov S. V.,  Dynamics of a Circular Cylinder and Two Point Vortices in a Perfect Fluid, Regular and Chaotic Dynamics, 2021, vol. 26, no. 6, pp. 675-691 DOI:10.1134/S156035472106006X
 Sokolov S. V., Ramodanov S. M. Falling Motion of a Circular Cylinder Interacting Dynamically with a Point Vortex 2013, vol. 18, no. 1-2, pp.  184-193 Abstract The dynamical behavior of a heavy circular cylinder and a point vortex in an unbounded volume of ideal liquid is considered. The liquid is assumed to be irrotational and at rest at infinity. The circulation about the cylinder is different from zero. The governing equations are Hamiltonian and admit an evident autonomous integral of motion — the horizontal component of the linear momentum. Using the integral we reduce the order and thereby obtain a system with two degrees of freedom. The stability of equilibrium solutions is investigated and some remarkable types of partial solutions of the system are presented. Keywords: point vortices, Hamiltonian systems, reduction, stability of equilibrium solutions Citation: Sokolov S. V., Ramodanov S. M.,  Falling Motion of a Circular Cylinder Interacting Dynamically with a Point Vortex, Regular and Chaotic Dynamics, 2013, vol. 18, no. 1-2, pp. 184-193 DOI:10.1134/S1560354713010139
 Ramodanov S. M., Tenenev V. A., Treschev D. V. Self-propulsion of a Body with Rigid Surface and Variable Coefficient of Lift in a Perfect Fluid 2012, vol. 17, no. 6, pp.  547-558 Abstract We study the system of a 2D rigid body moving in an unbounded volume of incompressible, vortex-free perfect fluid which is at rest at infinity. The body is equipped with a gyrostat and a so-called Flettner rotor. Due to the latter the body is subject to a lifting force (Magnus effect). The rotational velocities of the gyrostat and the rotor are assumed to be known functions of time (control inputs). The equations of motion are presented in the form of the Kirchhoff equations. The integrals of motion are given in the case of piecewise continuous control. Using these integrals we obtain a (reduced) system of first-order differential equations on the configuration space. Then an optimal control problem for several types of the inputs is solved using genetic algorithms. Keywords: perfect fluid, self-propulsion, Flettner rotor Citation: Ramodanov S. M., Tenenev V. A., Treschev D. V.,  Self-propulsion of a Body with Rigid Surface and Variable Coefficient of Lift in a Perfect Fluid, Regular and Chaotic Dynamics, 2012, vol. 17, no. 6, pp. 547-558 DOI:10.1134/S1560354712060068
 Borisov A. V., Mamaev I. S., Ramodanov S. M. Coupled motion of a rigid body and point vortices on a two-dimensional spherical surface 2010, vol. 15, no. 4-5, pp.  440-461 Abstract The paper is concerned with a class of problems which involves the dynamical interaction of a rigid body with point vortices on the surface of a two-dimensional sphere. The general approach to the 2D hydrodynamics is further developed. The problem of motion of a dynamically symmetric circular body interacting with a single vortex is shown to be integrable. Mass vortices on $S^2$ are introduced and the related issues (such as equations of motion, integrability, partial solutions, etc.) are discussed. This paper is a natural progression of the author’s previous research on interaction of rigid bodies and point vortices in a plane. Keywords: hydrodynamics on a sphere, coupled body-vortex system, mass vortex, equations of motion, integrability Citation: Borisov A. V., Mamaev I. S., Ramodanov S. M.,  Coupled motion of a rigid body and point vortices on a two-dimensional spherical surface, Regular and Chaotic Dynamics, 2010, vol. 15, no. 4-5, pp. 440-461 DOI:10.1134/S1560354710040040
 Borisov A. V., Mamaev I. S., Ramodanov S. M. Motion of a circular cylinder and $n$ point vortices in a perfect fluid 2003, vol. 8, no. 4, pp.  449-462 Abstract The paper studies the system of a rigid body interacting dynamically with point vortices in a perfect fluid. For arbitrary value of vortex strengths and circulation around the cylinder the system is shown to be Hamiltonian (the corresponding Poisson bracket structure is rather complicated). We also reduced the number of degrees of freedom of the system by two using the reduction by symmetry technique and performed a thorough qualitative analysis of the integrable system of a cylinder interacting with one vortex. Citation: Borisov A. V., Mamaev I. S., Ramodanov S. M.,  Motion of a circular cylinder and $n$ point vortices in a perfect fluid, Regular and Chaotic Dynamics, 2003, vol. 8, no. 4, pp. 449-462 DOI:10.1070/RD2003v008n04ABEH000257
 Ramodanov S. M. Motion of two circular cylinders in a perfect fluid 2003, vol. 8, no. 3, pp.  313-318 Abstract A planar analog of the Bjeknes problem of interaction of two spheres in a perfect fluid is considered. For the case of equal circulations around the cylinders, the equations of motion in the Poincare–Chetaev form are obtained, the integrals of motion are indicated. The problem is then reduced to a problem with two degrees of freedom. Most probably, this reduced problem is not integrable. Citation: Ramodanov S. M.,  Motion of two circular cylinders in a perfect fluid, Regular and Chaotic Dynamics, 2003, vol. 8, no. 3, pp. 313-318 DOI:10.1070/RD2003v008n03ABEH000247
 Ramodanov S. M. Motion of a Circular Cylinder and $N$ Point Vortices in a Perfect Fluid 2002, vol. 7, no. 3, pp.  291-298 Abstract The motion of a rigid circular cylinder and $N$ point vortices in an unbounded volume of perfect fluid is treated here on the basis of a potential framework. The formulas for the hydrodynamic force and moment acting upon a cylinder of arbitrary cross section are obtained. The equations governing the motion of a circular cylinder interacting with vortices are derived. For the greater part this paper coincides with  in which, however, only the case of one vortex was treated. It so happened that (due to a makeup man`s fault maybe)  was printed with no pictures in it. In this paper we reproduce those gures and extend the previous results. Citation: Ramodanov S. M.,  Motion of a Circular Cylinder and $N$ Point Vortices in a Perfect Fluid, Regular and Chaotic Dynamics, 2002, vol. 7, no. 3, pp. 291-298 DOI:10.1070/RD2002v007n03ABEH000211
 Ramodanov S. M. Motion of a Circular Cylinder and a Vortex in an Ideal Fluid 2001, vol. 6, no. 1, pp.  33-38 Abstract The motion of a circular cylinder and a point vortex in an unbounded ideal fluid is treated here on the basis of a potential framework. The formulas for the hydrodynamic force and moment acting upon a cylinder of arbitrary cross section are obtained. The equations governing the motion of a circular cylinder are derived and partially investigated. Citation: Ramodanov S. M.,  Motion of a Circular Cylinder and a Vortex in an Ideal Fluid, Regular and Chaotic Dynamics, 2001, vol. 6, no. 1, pp. 33-38 DOI:10.1070/RD2001v006n01ABEH000163