BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:S. P. Tsarev (Siberian Federal University\, Krasnoyarsk) DTSTART:20221222T110000Z DTEND:20221222T120000Z DTSTAMP:20260423T040334Z UID:mmandim/49 DESCRIPTION:Title: The Monge problem: From quadrature-free integration of underdetermined no nlinear ODEs to efficient car parking\nby S. P. Tsarev (Siberian Feder al University\, Krasnoyarsk) as part of Mathematical models and integratio n methods\n\n\nAbstract\nThis talk is about an old topic of finding closed -form solutions of UNDERDETERMINED systems of nonlinear ordinary different ial equations\, started by G.Monge in 1784 and later followed by Goursat ( 1905)\, Hilbert (1913) and Cartan (1914).\n\nIn the last decades of the XX century these problems draw attention of specialists in nonlinear control . In particular\, the technique of this problem was used in developing mot ion algorithms for nonholonomic mechanical systems\, a typical example bei ng a car with N trailers. Parking such a "car train" moving back is a popu lar difficult task! Modern results based on the old investigations of Gour sat make automatic control of such vehicles possible.\n\nFor those interes ted in the problem of integration of ODEs and PDEs: using the results desc ribed one can often remove (unnecessary) quadratures in the final expressi ons for the complete solution of a C-integrable nonlinear PDEs.\n\nWe expo se the classical results by Cartan and Hilbert showing the intruiging deta ils of the Monge problem.\n LOCATION:https://researchseminars.org/talk/mmandim/49/ END:VEVENT END:VCALENDAR