Geodesic
Invariant measure and hamiltonization of nonholonomic systems
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 3, pp. 355-359.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper discusses new unresolved problems of nonholonomic mechanics. Hypotheses of the possibility of Hamiltonization and the existence of an invariant measure for such systems are advanced.
Keywords: nonholonomic mechanics, tensor invariant, invariant measure
Mots-clés : Poisson structure. 
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Alexey V. Borisov; Ivan S. Mamaev. Invariant measure and hamiltonization of nonholonomic systems. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 3, pp. 355-359. http://geodesic.mathdoc.fr/item/ND_2014_10_3_a8/

[1] Bolsinov A. V., Borisov A. V., Mamaev I. S., “Gamiltonizatsiya negolonomnykh sistem v okrestnosti invariantnykh mnogoobrazii”, Nelineinaya dinamika, 6:4 (2010), 829–854 ; Bolsinov A. V., Borisov A. V., Mamaev I. S., “Hamiltonization of nonholonomic systems in the neighborhood of invariant manifolds”, Regul. Chaotic Dyn., 16:5 (2011), 443–464 | DOI | MR

[2] Borisov A. V., Mamaev I. S., “Gamiltonovost zadachi Chaplygina o kachenii shara”, Matem. zametki, 70:5 (2001), 793–795 | DOI | MR | Zbl

[3] Tsyganov A. V., “O puassonovykh strukturakh, voznikayuschikh pri rassmotrenii shara Chaplygina i ego obobschenii”, Nelineinaya dinamika, 8:2 (2012), 345–353

[4] Borisov A. V., Mamaev I. S., Bizyaev I. A., “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinamika, 9:2 (2013), 141–202

[5] Borisov A. V., Mamaev I. S., “Prepyatstvie k gamiltonovosti negolonomnykh sistem”, Dokl. RAN, 387:6 (2002), 764–766

[6] Borisov A. V., Mamaev I. S., “The rolling motion of a rigid body on a plane and a sphere: Hierarchy of dynamics”, Regul. Chaotic Dyn., 7:2 (2002), 177–200 | DOI | MR | Zbl

[7] Bolsinov A. V., Borisov A. V., Mamaev I. S., “Kachenie bez vercheniya shara po ploskosti: otsutstvie invariantnoi mery v sisteme s polnym naborom integralov”, Nelineinaya dinamika, 8:3 (2012), 605–616

[8] Borisov A. V., Mamaev I. S., Kilin A. A., “The rolling motion of a ball on a surface: New integrals and hierarchy of dynamics”, Regul. Chaotic Dyn., 7:2 (2002), 201–219 | DOI | MR | Zbl

[9] Borisov A. V., Mamaev I. S., “O nesuschestvovanii invariantnoi mery pri kachenii neodnorodnogo ellipsoida po ploskosti”, Matem. zametki, 77:6 (2005), 930–931 | DOI