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SUMMARY:Maksim Gadzhiev and Alexander Kuleshov
DTSTART:20230531T162000Z
DTEND:20230531T180000Z
DTSTAMP:20260423T023017Z
UID:GDEq/91
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/91/">In
 tegrability of the problem of motion of a body with a fixed point in a flo
 w of particles</a>\nby Maksim Gadzhiev and Alexander Kuleshov as part of G
 eometry of differential equations seminar\n\nLecture held in room 303 of t
 he Independent University of Moscow.\n\nAbstract\nThe problem of the motio
 n\, 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 spa
 rse\, there is no interaction between the particles. Based on the approach
  proposed by V.V. Beletsky\, an expression is obtained for the moment of f
 orces 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 o
 f 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. Co
 nstraints on the system parameters are obtained under which there are inte
 grable cases corresponding to the classical Euler-Poinsot\, Lagrange and H
 ess cases of integrability of the equations of motion of a heavy rigid bod
 y with a fixed point. The case when the surface of the body is an ellipsoi
 d 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.\n
LOCATION:https://researchseminars.org/talk/GDEq/91/
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