Seminar talk, 31 May 2023: Difference between revisions
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| speaker1 = Maksim Gadzhiev | | speaker1 = Maksim Gadzhiev | ||
| speaker2 = Alexander Kuleshov | | speaker2 = Alexander Kuleshov | ||
| title = Integrability of the problem of | | title = Integrability of the problem of motion of a body with a fixed point in a flow of particles | ||
| abstract = The problem of the motion, in the free molecular flow of particles, of a rigid body with a fixed point is considered. The molecular flow is assumed to be sufficiently sparse, there is no interaction between the particles. Based on the approach proposed by V.V. Beletsky, an expression is obtained for the moment of forces acting on a body with a fixed point. It is shown that the equations of motion of a body are similar to the classical Euler-Poisson equations of motion of a heavy rigid body with a fixed point and are presented in the form of classical Euler-Poisson equations in the case when the surface of a body is a sphere. The existence of the first integrals is discussed. Constraints on the system parameters are obtained under which there are integrable cases corresponding to the classical Euler-Poinsot, Lagrange and Hess cases of integrability of the equations of motion of a heavy rigid body with a fixed point. The case when the surface of the body is an ellipsoid is considered. Using the methods developed in the works of V.V. Kozlov, proved the absence of an integrable case in this problem, similar to the Kovalevskaya case. | | abstract = The problem of the motion, in the free molecular flow of particles, of a rigid body with a fixed point is considered. The molecular flow is assumed to be sufficiently sparse, there is no interaction between the particles. Based on the approach proposed by V.V. Beletsky, an expression is obtained for the moment of forces acting on a body with a fixed point. It is shown that the equations of motion of a body are similar to the classical Euler-Poisson equations of motion of a heavy rigid body with a fixed point and are presented in the form of classical Euler-Poisson equations in the case when the surface of a body is a sphere. The existence of the first integrals is discussed. Constraints on the system parameters are obtained under which there are integrable cases corresponding to the classical Euler-Poinsot, Lagrange and Hess cases of integrability of the equations of motion of a heavy rigid body with a fixed point. The case when the surface of the body is an ellipsoid is considered. Using the methods developed in the works of V.V. Kozlov, proved the absence of an integrable case in this problem, similar to the Kovalevskaya case. | ||
| video = | | video = | ||
Revision as of 10:01, 2 May 2023
Speakers: Maksim Gadzhiev and Alexander Kuleshov
Title: Integrability of the problem of motion of a body with a fixed point in a flow of particles
Abstract:
The problem of the motion, in the free molecular flow of particles, of a rigid body with a fixed point is considered. The molecular flow is assumed to be sufficiently sparse, there is no interaction between the particles. Based on the approach proposed by V.V. Beletsky, an expression is obtained for the moment of forces acting on a body with a fixed point. It is shown that the equations of motion of a body are similar to the classical Euler-Poisson equations of motion of a heavy rigid body with a fixed point and are presented in the form of classical Euler-Poisson equations in the case when the surface of a body is a sphere. The existence of the first integrals is discussed. Constraints on the system parameters are obtained under which there are integrable cases corresponding to the classical Euler-Poinsot, Lagrange and Hess cases of integrability of the equations of motion of a heavy rigid body with a fixed point. The case when the surface of the body is an ellipsoid is considered. Using the methods developed in the works of V.V. Kozlov, proved the absence of an integrable case in this problem, similar to the Kovalevskaya case.