BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Kuleshov DTSTART:20260325T162000Z DTEND:20260325T180000Z DTSTAMP:20260423T041811Z UID:GDEq/154 DESCRIPTION:Title: E xact solutions of some problems of rigid body dynamics\nby Alexander K uleshov as part of Geometry of differential equations seminar\n\nLecture h eld in room 303 of the Independent University of Moscow.\n\nAbstract\nInte rest in integrable problems in mechanics has never waned. Finding new inte grable cases of differential equations of motion for various mechanical sy stems\, as well as finding solutions in quadratures for these cases\, is o ne of the main problem of theoretical mechanics. The problem of exact inte gration of differential equations of motion has several aspects. The geome tric aspect is associated with the qualitative study of the regular behavi or of the trajectories of integrable systems. The constructive aspect is a ssociated with finding the conditions under which an algorithm for explici t solving differential equations using quadratures can be specified. In th is regard\, another important aspect of the range of issues under consider ation arises: the explicit solution of systems of differential equations. For certain classes of differential equations\, relying on their specific structure\, special methods can be used. An example here is the broad and important class of linear differential equations. The study of many proble ms in mechanics and mathematical physics reduces to solving a second-order linear homogeneous differential equation. If\, by changing the independen t variable\, it is possible to reduce the corresponding second-order linea r differential equation to an equation with rational coefficients\, then t he necessary and sufficient for solvability by quadratures for such an equ ation are determined by the so-called Kovacic algorithm. In 1986\, the Ame rican mathematician J. Kovacic presented an algorithm for finding Liouvill ian solutions of a second-order linear homogeneous differential equation w ith rational coefficients. If the differential equation has no Liouvillian solution\, the algorithm also allows one to establish this fact.\n\nThis talk will discuss the application of the Kovacic algorithm to investigate the existence of Liouvillian solutions in the problem of motion of a rotat ionally symmetric rigid body on a perfectly rough plane and on a perfectly rough sphere. It will also discuss the application of the algorithm to in vestigate the existence of Liouvillian solutions in the problem of motion of a heavy homogeneous ball on a fixed perfectly rough surface of revoluti on. The existence of Liouvillian solutions in the Hess case of the problem of motion of a heavy rigid body with a fixed point is also analyzed.\n LOCATION:https://researchseminars.org/talk/GDEq/154/ END:VEVENT END:VCALENDAR