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@article{FPM_2005_11_7_a9, author = {V. I. Kalenova and A. V. Karapetyan and V. M. Morozov and M. A. Salmina}, title = {Nonholonomic mechanical systems and stabilization of motion}, journal = {Fundamentalʹna\^a i prikladna\^a matematika}, pages = {117--158}, publisher = {mathdoc}, volume = {11}, number = {7}, year = {2005}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_7_a9/} }
TY - JOUR AU - V. I. Kalenova AU - A. V. Karapetyan AU - V. M. Morozov AU - M. A. Salmina TI - Nonholonomic mechanical systems and stabilization of motion JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2005 SP - 117 EP - 158 VL - 11 IS - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2005_11_7_a9/ LA - ru ID - FPM_2005_11_7_a9 ER -
%0 Journal Article %A V. I. Kalenova %A A. V. Karapetyan %A V. M. Morozov %A M. A. Salmina %T Nonholonomic mechanical systems and stabilization of motion %J Fundamentalʹnaâ i prikladnaâ matematika %D 2005 %P 117-158 %V 11 %N 7 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2005_11_7_a9/ %G ru %F FPM_2005_11_7_a9
V. I. Kalenova; A. V. Karapetyan; V. M. Morozov; M. A. Salmina. Nonholonomic mechanical systems and stabilization of motion. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 7, pp. 117-158. http://geodesic.mathdoc.fr/item/FPM_2005_11_7_a9/
[1] Budanov V. M., Devyanin E. A., “O dvizhenii kolësnykh robotov”, PMM, 67:2 (2003), 244–255 | MR | Zbl
[2] Voronets P. V., Uravneniya dvizheniya tvërdogo tela, katyaschegosya bez skolzheniya po nepodvizhnoi poverkhnosti, Tip. Un-ta Sv. Vladimira, Kiev, 1903
[3] Zegzhda S. A., Soltakhanov Sh. Kh., Yushkov M. P., Uravneniya dvizheniya negolonomnykh sistem i variatsionnye printsipy mekhaniki, Izd-vo Sankt-Peterburgskogo un-ta, SPb., 2002
[4] Zobova A. A., “Postroenie diagramm Puankare–Chetaeva i Smeila v zadache o dvizhenii tela vrascheniya na sherokhovatoi ploskosti”, Mobilnye roboty i mekhatronnye sistemy, Izd-vo Mosk. un-ta, M., 2004, 107–139 | MR
[5] Kalënova V. I., Morozov V. M., “K voprosu ob ustoichivosti statsionarnykh dvizhenii negolonomnykh sistem Chaplygina”, PMM, 66:2 (2002), 192–199 | MR | Zbl
[6] Kalënova V. I., Morozov V. M., “Ob ustoichivosti ustanovivshikhsya dvizhenii negolonomnykh mekhanicheskikh sistem s tsiklicheskimi koordinatami”, PMM, 68:2 (2004), 195–205 | MR | Zbl
[7] Kalënova V. I., Morozov V. M., Salmina M. A., “K zadache stabilizatsii ustanovivshikhsya dvizhenii sistem s tsiklicheskimi koordinatami”, PMM, 53:5 (1989), 714–867 | MR
[8] Kalënova V. I., Morozov V. M., Salmina M. A., “Upravlyaemost i nablyudaemost v zadache stabilizatsii mekhanicheskikh sistem s tsiklicheskimi koordinatami”, PMM, 56:6 (1992), 959–967 | MR | Zbl
[9] Kalënova V. I., Morozov V. M., Salmina M. A., “Ustoichivost i stabilizatsiya statsionarnykh dvizhenii negolonomnykh mekhanicheskikh sistem odnogo klassa”, Mobilnye roboty i mekhatronnye sistemy, Izd-vo Mosk. un-ta, M., 2004, 119–134
[10] Kalënova V. I., Morozov V. M., Shevelëva E. N., Ustoichivost i stabilizatsiya dvizheniya odnokolësnogo ekipazha (monotsikla) Mobilnye roboty i mekhatronnye sistemy, Izd-vo Mosk. un-ta, M., 1999
[11] Kalënova V. I., Morozov V. M., Shevelëva E. N., “Upravlyaemost i nablyudaemost v zadache stabilizatsii ustanovivshikhsya dvizhenii negolonomnykh mekhanicheskikh sistem s tsiklicheskimi koordinatami”, PMM, 65:6 (2001), 915–924 | MR | Zbl
[12] Kalënova V. I., Morozov V. M., Shevelëva E. N., “Ustoichivost i stabilizatsiya dvizheniya odnokolësnogo velosipeda”, Izv. RAN. MTT, 2001, no. 4, 49–58
[13] Kalman D., Fal P., Arbib M., Ocherki po matematicheskoi teorii sistem, Mir, M., 1971 | MR | Zbl
[14] Karapetyan A. V., “Ob ustoichivosti statsionarnykh dvizhenii negolonomnykh sistem Chaplygina”, PMM, 42:5 (1978), 801–807 | MR | Zbl
[15] Karapetyan A. V., “K voprosu ob ustoichivosti statsionarnykh dvizhenii negolonomnykh sistem”, PMM, 44:3 (1980), 418–426 | MR | Zbl
[16] Karapetyan A. V., “Ob ustoichivosti statsionarnykh dvizhenii sistem nekotorogo vida”, Izv. AN SSSR. MTT, 1983, no. 2, 45–52 | MR
[17] Karapetyan A. V., Ustoichivost statsionarnykh dvizhenii, Editorial URSS, M., 1988
[18] Karapetyan A. V., “O spetsifike primeneniya teorii Rausa k sistemam s differentsialnymi svyazyami”, PMM, 58:3 (1994), 17–22 | MR | Zbl
[19] Karapetyan A. V., Kuleshov A. S., “Metody issledovaniya ustoichivosti i bifurkatsii statsionarnykh dvizhenii konservativnykh negolonomnykh sistem”, Problemy mekhaniki, Fizmatlit, M., 2003, 429–464
[20] Karapetyan A. V., Rumyantsev V. V., Ustoichivost konservativnykh i dissipativnykh sistem, Itogi nauki i tekhniki. Ser. Obschaya mekhanika, 6, VINITI, M., 1983
[21] Kuleshov A. S., K dinamike volchka na sherokhovatoi ploskosti, VTs RAN, M., 1999 | MR
[22] Kuleshov A. S., “Elementarnoe izlozhenie dinamiki sneikborda”, Mobilnye roboty i mekhatronnye sistemy, Izd-vo Mosk. un-ta, M., 2004, 159–166
[23] Lobas L. G., Negolonomnye modeli kolësnykh ekipazhei, Naukova dumka, Kiev, 1986 | MR | Zbl
[24] Lure A. I., Analiticheskaya mekhanika, Fizmatgiz, M., 1961 | MR
[25] Lyapunov A. M., O postoyannykh vintovykh dvizheniyakh tvërdogo tela v zhidkosti, Izd-vo Kharkovskogo mat. obsch-va, Kharkov, 1888
[26] Lyapunov A. M., Obschaya zadacha ob ustoichivosti dvizheniya, Izd-vo Kharkovskogo mat. obsch-va, Kharkov, 1892
[27] Malkin I. G., Teoriya ustoichivosti dvizheniya, Nauka, M., 1966 | MR | Zbl
[28] Markeev A. P., Dinamika tela, soprikasayuschegosya s tvërdoi poverkhnostyu, Nauka, M., 1992 | MR | Zbl
[29] Martynenko Yu. G., Orlov I. V., “Vliyanie perekhodnykh protsessov v elektroprivode na ustoichivost dvizheniya mobilnogo kolësnogo robota”, Mobilnye roboty i mekhatronnye sistemy, Izd-vo Mosk. un-ta, M., 2004, 135–149
[30] Mindlin I. M., Pozharitskii G. K., “Ob ustoichivosti statsionarnykh dvizhenii tyazhëlogo tela vrascheniya na absolyutno sherokhovatoi gorizontalnoi ploskosti”, PMM, 29:4 (1965), 742–745 | Zbl
[31] Morozov V. M., Kozhanov A. A., “Statsionarnye dvizheniya odnokolësnogo ekipazha i ikh ustoichivost”, Mobilnye roboty i mekhatronnye sistemy, Izd-vo Mosk. un-ta, M., 2002, 132–141
[32] Morozov V. M., Nazarenko A. Yu., Mobilnye roboty i mekhatronnye sistemy, Izd-vo Mosk. un-ta, M., 2001, 227–237
[33] Borisov A. V., Mamaev I. S. (red.), Negolonomnye dinamicheskie sistemy, Moskva; Izhevsk, 2002 | MR
[34] Neimark Yu. I, Fufaev N. A., Dinamika negolonomnykh sistem, Nauka, M., 1967
[35] Rumyantsev V. V., “Ob upravlenii i stabilizatsii sistem s tsiklicheskimi koordinatami”, PMM, 36:6 (1972), 966–976 | Zbl
[36] Rumyantsev V. V., “Ob ustoichivosti vrascheniya tyazhëlogo girostata na gorizontalnoi ploskosti”, Izv. AN SSSR. MTT, 1980, no. 4, 11–21 | MR
[37] Chaplygin S. A., Issledovaniya po dinamike negolonomnykh sistem, Gostekhizdat, M.–L., 1949
[38] Chetaev N. G., Ustoichivost dvizheniya. Raboty po analiticheskoi mekhanike, Izd-vo AN SSSR, M., 1962 | MR
[39] Abraham R., Marsden J., Foundations of Mechanics, Benjamin, New York–Amsterdam, 1978 | MR | Zbl
[40] Bloch A. M., “Stability of nonholonomic control systems”, Automatica, 28:2 (1992), 431–435 | DOI | MR | Zbl
[41] Bloch A. M., Krishnaprasad P. S., Marsden J. E., Murray R., “Nonholonomic mechanical systems with symmetry”, Arch. Rational Mech. Anal., 136 (1996), 21–99 | DOI | MR | Zbl
[42] Bloch A. M., McClamroch N. H., “Control and stabilization of nonhoionomic Chaplygin dynamic systems”, Proc. IEEE Conf. Decision Control, Brighton, UK, 1991, 1127–1132
[43] Bloch A. M., Reyhanoglu M., McClamroch N. H., “Control and stabilization of nonholonomic dynamic system”, IEEE Trans. Automat. Control, 37:11 (1992), 1746–1757 | DOI | MR | Zbl
[44] Hautis M. L. J., “Controllability and observability conditions of linear autonomous systems”, Proc. Konink. Nederl. Akad. Wetensch. Ser. A, 72 (1969), 443–448 | MR
[45] Karapetyan A. V., Kuleshov A. S., “Steady motions of nonholonomic systems”, Regular Chaotic Dynamics, 7:1 (2002) | MR | Zbl
[46] Laub A. J., Arnold W. F., “Controllability and observability criteria for multivariable linear second-order models”, IEEE Trans. Automat. Control, 29:2 (1984), 163–165 | DOI | MR | Zbl
[47] Levi-Civita T., “Sur la recherche des solutions particulieres des systemes differentiels et sur les mouvements stationnaires”, Prace Math. Fis., 17 (1906), 1–140
[48] Poincare H., “Sur l'equilibre d'une masse fluide animee d'un mouvement de rotation”, Acta Math., 7 (1885), 259–380 | DOI | MR
[49] Routh E. J., A Treatise on the Stability of a Given State of Motion, MacMillan and Co, London, 1877
[50] Routh E. J., The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies, MacMillan and Co., London, 1884
[51] Smale S., “Topology and mechanics”, Invent. Math., 10 (1970), 305–311 | DOI | MR
[52] Zenkov D. V., Bloch A. M, Leonard N. E., Marsden J. E., “Matching and stabilization of the unicycle with rider”, Proc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, 2000, 187–188
[53] Zenkov D. V., Bloch A. M., Marsden J. E., “The energy-momentum method for the stability of nonholonomic systems”, Dynam. Stability Systems, 13 (1998), 123–166 | MR
[54] Zenkov D. V., Bloch A. M., Marsden J. E., “Stabilization of the unicycle with rider”, Proc. CDC, 38 (1999), 3470–3471 | MR
[55] Zenkov D. V., Bloch A. M., Marsden J. E., “The Luapunov–Malkin theorem and stabilization of the unicycle with rider”, Systems and Control Letters, 45 (2002), 293–302 | DOI | MR | Zbl