Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems

Borisov, A.V. and Mamaev, I.S., The Rolling of Rigid Body on a Plane and Sphere. Hierarchy of Dynamics, Regul. Chaotic Dyn., 2002, vol. 7, no. 1, pp. 177–200.

Borisov, A.V., Mamaev, I.S., and Kilin, A.A., Rolling of a Ball on a Surface. New Integrals and Hierarchy of Dynamics, Regul. Chaotic Dyn., 2002, vol. 7, no. 2, pp. 201–220.

Ferrers, N.M., Extension of Lagrange’s Equations, Quart. J. Pure Appl. Math., 1872, vol. 12, no. 45, pp. 1–5.

Sumbatov, A.S., Nonholonomic Systems, Regul. Chaotic Dyn., 2002, vol. 7, no. 2, pp. 221–238.

Benenti, S., A “User-Friendly” Approach to the Dynamical Equations of Nonholonomic Systems, SIGMA, 2007, vol. 3, 036 (33 pages).

Woronetz, P.V., On Equations of Motion of Nonholonomic Systems, Matematicheskii sbornik (Mathematical Collection), 1901, vol. 22, no. 4, pp. 659–686 (in Russian).

Woronetz, P.V., Equations of Motion of a Rigid Body Rolling along a Stationary Surface Without Slipping, Kiev: Proc. of Kiev University, 1903, vol. 43, no. 1, pp. 1–66.

Woronetz, P.V., Transformation of Equations of Motion with the Help of Linear Integrals (with Application to the 3-Body Problem), Kiev: Proc. of Kiev University, 1907, vol. 47, no. 1–2, pp. 1–192.

Woronetz, P., Über die rollende Bewegung einer Kreisscheibe auf einer beliebigen Flache unter der Wirkung von gegebenen Kraften Math. Annalen, 1909, vol. 67, pp. 268–280.

Woronetz, P., Über die Bewegung eines starren Körpers, der ohne Gleitung auf einer beliebigen Fläche rollt, Math. Annalen, 1911, vol. 70, pp. 410–453.

Woronetz, P., Über die Bewegungsgleichungen eines starren Körpers, Math. Annalen, 1912, vol. 71, pp. 392–403.

Arnold V.I., Kozlov V.V., and Neishtadt A.I. Mathematical Aspects of Classical and Celestial Mechanics, Itogi Nauki i Tekhniki. Sovr. Probl. Mat. Fundamental’nye Napravleniya, Vol. 3, VINITI, Moscow 1985. English transl.: Encyclopadia of Math. Sciences, Vol. 3, Berlin: Springer-Verlag, 1989.

Borisov, A.V. and Mamaev, I.S., Chaplygin’s Ball. The Suslov Problem and Veselova’s Problem. Integrability and Realization of Constraints, in (Nonholonomic Dynamical Systems), Borisov, A.V. and Mamaev, I.S., Eds., Moscow-Izhevsk: RCD, Institute of Computer Sciences, 2002, pp. 118–130.

Ehlers, K. and Koiller, J., Rubber Rolling: Geometry and Dynamics of 2-3-5 Distributions, in Proceedings IUTAM symposium 2006 on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25–30 August, 2006), pp. 469–480.

Chaplygin, S.A., On a Ball’s Rolling on a Horizontal Plane, Matematicheskiĭ sbornik (Mathematical Collection), 1903, vol. 24. [English translation: Regul. Chaotic Dyn., 2002, vol. 7, no. 2, pp. 131–148. http://ics.org.ru/eng?menu=mi_pubs&abstract=312 .]

Veselova, L.E., New Cases of the Integrability of the Equations of Motion of a Rigid Body in the Presence of a Nonholonomic Constraint, in Geometry, Differential Equations and Mechanics, Moskov. Gos. Univ., Mekh.-Mat. Fak., Moscow, 1986, pp. 64–68.

Rashevsky, P.K., About Connecting Two Points of a Completely Nonholonomic Space by Admissible Curve, Uch. Zap. Ped. Inst. im. Liebknechta, Ser. Phys. Math., 1938, no. 2, pp. 83–94.

Chow, W.L., Über Systeme von linearen partiellen Differential Gleichungen erster Ordnung, Math. Ann., 1939, vol. 117, pp. 98–105.

Agrachev, A.A., Rolling Balls and Octonions, Proc. Steklov Institute of Mathematics, 2007, vol. 258, pp. 13–22 [Tr. Mat. Inst. Steklova, 2007, vol. 258, pp. 17–27].

Bor, G. and Montgomery, R., G 2 and the “Rolling Distribution”, arXiv:math.DG/0612469v1.

Chaplygin, S.A., On the Theory of Motion of Nonholonomic Systems. Example of Application of the Reducing Mutiplier Method, unpublished note; printed in Collected Papers, Moscow-Leningrad: Gostekhizdat, 1948, Vol. 3, pp. 248–275.

Suslov, G.K., Teoreticheskaya mekhanika (Theoretical Mechanics), Moscow-Leningrad: Gostekhizdat, 1946.

Zhuravlev, V.F., On a Model of a Dry Friction in Problems of Rigid Body Dynamics, Adv. in Mech., 2005, no. 3, pp. 58–76 (in Russian).

Kozlov, V.V., On the Existence of an Integral Invariant of a Smooth Dynamic System, J. Appl. Math. Mech., 1987, vol. 51, no. 4, pp. 420–426 [Prikl. Mat. Mekh., 1987, vol. 51, no. 4, pp. 538–545].

Kolmogorov, A.N., On Dynamical Systems with an Integral Invariant on the Torus, Doklady Akad. Nauk SSSR, 1953, vol. 93, pp. 763–766 (in Russian).

Borisov, A.V. and Mamaev, I.S., Strange Attractors in Rattleback Dynamics, Uspehi Fiz. Nauk, 2003, vol. 173, no. 4, pp. 407–418 [Physics-Uspekhi, 2003, vol. 46, no. 4, pp. 393–403].

Veselov, A.P. and Veselova, L.E., Integrable Nonholonomic Systems on Lie Groups, Math. Notes, 1988, vol. 44, no. 5–6, pp. 810–819 [Mat. Zametki, 1988, vol. 44, no. 5, pp. 604–619].

Kozlov, V.V., On the Integration Theory of Equations of Nonholonomic Mechanics, Adv. in Mech., 1985, vol. 8, no. 3, pp. 85–107 (in Russian). See also: Regul. Chaotic Dyn., 2002, vol. 7, no. 2, pp. 191–176.

Borisov, A.V. and Mamaev, I.S., Puassonovy struktury i algebry Li v gamil’tonovoi mekhanike (Poisson Structures and Lie Algebras in Hamiltonian Mechanics), vol. 7 of Library “R & C Dynamics”, Izhevsk, 1999.

Tatarinov, Ya.V., Separation of Variables and New Topological Phenomena in Holonomic and Nonholonomic Systems, Trudy Sem. Vektor. Tenzor. Anal., 1988, no. 23, pp. 160–174 (in Russian).

Novikov, S.P. and Taimanov, I.A., Modern Geometric Structures and Fields, vol. 71 of Graduate Studies in Mathematics, Providence, RI: AMS, 2006.

Olver, P.J., Applications of Lie Groups to Differential Equations, 2nd ed., vol. 107 of Graduate Texts in Mathematics, New York: Springer-Verlag, 1993.

Painlevé, P., Lecons sur le frottement, P.: Hermann, 1895.

Weinstein, A., Poisson Geometry, Diff. Geom. Appl., 1998, vol. 9, no. 1–2, pp. 213–238.

Borisov, A.V. and Dudoladov, S.L., Kovalevskaya Exponents and Poisson Structures, Regul. Chaotic Dyn., 1999, vol. 4, no. 3, pp. 13–20.

Kozlov, V.V., Symmetries, Topology and Resonances in Hamiltonian Mechanics, Berlin: Springer-Verlag, 1996.

Borisov, A.V. and Mamaev, I.S., Dinamika tverdogo tela. Gamiltonovy metody, integriruemost’, khaos (Rigid Body Dynamics. Hamiltonian Methods, Integrability, Chaos), Moscow-Izhevsk: Inst. komp. issled., RCD, 2005.

Chaplygin, S.A., On a Motion of a Heavy Body of Revolution on a Horizontal Plane, Trudy Otdeleniya fizicheskikh nauk Obshchestva lyubiteleĭ estestvoznaniya (Transactions of the Physical Section of Moscow Society of Friends of Natural Scientists), 1897, vol. 9, no. 1 [English translation: Regul. Chaotic Dyn., 2002, vol. 7, no. 2, pp. 119–130; http://ics.org.ru/eng?menu=mi_pubs&abstract=311 .]

Gallop, M.A., On the Rise of a Spinning Top, Trans. Cambridge Phil. Society, 1904, vol. 19, pp. 356–373.

Ramos, A., Poisson Structures for Reduced Non-holonomic Systems, J. Phys. A, 2004, vol. 37, no. 17, pp. 4821–4842.

Fassò, F., Giacobbe, A., and Sansonetto, N., Periodic Flows, Rank-Two Poisson Structures, and Nonholonomic Mechanics, Regul. Chaotic Dyn., 2005, vol. 10, no. 3, pp. 267–284.

Tatarinov, Ya.V., Construction of Compact Invariant Manifolds, not Diffeomorphic to Tori, in One Integrable Nonholonomic Problem, Uspekhi Matem. Nauk, no. 5, page 216 (in Russian).

Bates, L. and Cushman, R., What is a Completely Integrable Nonholonomic Dynamical System? Rep. on Math. Phys., 1999, vol. 44, no. 1–2, pp. 29–35.

Sinai, Ya.G., Introduction to Ergodic Theory, vol. 18 of Mathematical Notes, Princeton, N.J.: Princeton University Press, 1976.

Kornfel’d, I.P., Sinai, Ya.G., and Fomin, S.V., Ergodicheskaya teoriya (Ergodic Theory), Moscow: Nauka, 1980.

Borisov, A.V. and Mamaev, I.S., Obstacle to the Reduction of Nonholonomic Systems to the Hamiltonian Form, Dokl. Phys., 2002, vol. 47, no. 12, pp. 892–894 [Dokl. Akad. Nauk, 2002, vol. 387, no. 6, pp. 764–766].

Kozlov, V.V., Diffusion in Systems with Integral Invariants on the Torus, Dokl. Math., 2001, vol. 64, no. 3, pp. 390–392 [Dokl. Akad. Nauk, 2001, vol. 381, no. 5, pp. 596–598].

Bolsinov, A.V. and Fomenko, A.T., Integrable Hamiltonian Systems: Geometry, Topology, Classification, CRC Press, 2004.

Chaplygin, S.A., On the Theory of Motion of Nonholonomic Systems. The Reducing-Multiplier Theorem, Matematicheskii sbornik (Mathematical Collection), 1911, vol. 28, no. 1 [English translation: Regul. Chaotic Dyn., 2008, vol. 13, no. 4, pp. 369–376; http://ics.org.ru/eng?menu=mi_pubs&abstract=1303 ].

Cantrijin, F., de Léon, M., and de Diego, D., On the Geometry of Generalized Chaplygin Systems, Math. Proc. Camb. Phil. Soc., 2002, vol. 132, pp. 323–351.

Koiller, J., Reduction of Some Classical Nonholonomic Systems with Symmetry, Arch. Rational. Mech. Anal., 1992, vol. 118, pp. 113–148.

Fedorov, Yu.N. and Jovanović, B., Nongholonomic LR-Systems as Generalized Chaplygin Systems with an Invariant Measure and Flows on Homogeneous Spaces, J. of Nonlinear Science, 2004, vol. 14, pp. 341–381.

Moshchuk, N.K., Reducing the Equations of Motion of Certain Nonholonomic Chaplygin Systems to Lagrangian and Hamiltonian Form, J. Appl. Math. Mech., 1987, vol. 51, no. 2, pp. 172–177 [Prikl. Mat. Mekh., 1987, vol. 51, no. 2, pp. 223–229].

Rumyantsev, V.V. and Sumbatov, A.V., On the Problem of Generalization of the Hamilton-Jacobi Method for Non-holonomic System, ZAMM, 1978, vol. 58, pp. 477–781.

Dragovic, V., Gajic, B., and Jovanovic, B., Generalizations of Classical Integrable Nonholonomic Rigid Body Systems, J. Phys. A: Math. Gen., 1998, vol. 31, pp. 9861–9869.

Kharlamova-Zabelina, E.I., Rapid Rotation of a Rigid Body about a Fixed Point under the Presence of a Nonholonomic Constraint, Vestnik Moskov. Univ. Ser. Mat. Mekh. Astron. Fiz. Khim., 1957, vol. 12, no. 6, pp. 25–34 (in Russian).

Kharlamov, A.P., The Inertial Motion of a Body with a Fixed Point and Subject to a Nonholonomic Constraint, Mekh. Tverd. Tela, Donetsk, 1995, no. 27, pp. 21–31 (in Russian).

Bloch, A.M., Nonholonomic Mechanics and Control. With the collaboration of Baillieul, J., Crouch, P., and Marsden, J. With scientific input from Krishnaprasad, P.S., Murray, R.M., and Zenkov, D., vol. 24 of Interdisciplinary Applied Mathematics, Systems and Control, New York: Springer-Verlag, 2003.

Fedorov, Yu.N., Two Integrable Nonholonomic Systems in Classical Dynamics, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1989, no. 4, pp. 38–41 (in Russian).

Kilin, A.A., The Dynamics of Chaplygin ball: the Qualitative and Computer Analisis, Regul. Chaotic Dyn., 2001, vol. 6, no. 3, pp. 291–306.

Schneider, D.A., Non-holonomic Euler-Poincaré Equations and Stability in Chaplygin’s Sphere, Dyn. Sys., 2002, vol. 17, no. 2, pp. 87–130.

Markeev, A.P., Integrability of a Problem on Rolling of Ball with Multiply Connected Cavity Filled by Ideal Liquid, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 1986, vol. 21, no. 1, pp. 64–65 (in Russian).

Duistermaat, J.J., Chaplygin’s Sphere, in Cushman, R., Duistermaat, J.J., and Śniatycki, J., Chaplygin and the Geometry of Nonholonomically Constrained Systems (in preparation), 2000; arXiv:math.DS/0409019.

Borisov, A.V. and Mamaev, I.S., The Chaplygin Problem of the Rolling Motion of a Ball Is Hamiltonian, Math. Notes, 2001, vol. 70, no. 5, pp. 720–723 [Mat. Zametki, 2001, vol. 70, no. 5, pp. 793–796].

Ehlers, K., Koiller, J., Montgomery, R., and Rios, P.M., Nonholonomic Systems via Moving Frames: Cartan Equivalence and Chaplygin Hamiltonization. The Breadth of Symplectic and Poisson Geometry, vol. 232 of Progr. Math., Boston, MA: Birkhäuser Boston, 2005, pp. 75–120.

Garcia-Naranjo, L., Reduction of Almost Poisson Brackets for Nonholonomic Systems on Lie Groups, Regul. Chaotic Dyn., 2007, vol. 12, no. 4, pp. 365–388.

Kozlov, V.V. and Fedorov, Yu.N., A Memoir on Integrable Systems, Springer-Verlag (in preparation).

Borisov, A.V. and Fedorov, Y.N., On Two Modified Integrable Problems of Dynamics, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1995, no. 6, pp. 102–105 (in Russian).

Contensou, P., Couplage entre frottement de glissement et frottement de pivotement dans la théorie de la toupie, Kreiselprobleme Gydrodynamics: IUTAM Symp. Celerina, Berlin: Springer, 1963, pp. 201–216.

Yaroshchuk, V.A., New Cases of the Existence of an Integral Invariant in a Problem on the Rolling of a Rigid Body, Without Slippage, on a Fixed Surface, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1992, no. 6, pp. 26–30 (in Russian).

Borisov, A.V. and Mamaev, I.S., Rolling of a Non-homogeneous Ball over a Sphere Without Slipping and Twisting, Regul. Chaotic Dyn., 2007, vol. 12, no. 2, pp. 153–159.

Borisov, A.V., Mamaev I.S., and Marikhin, V.G., Explicit Integration of One Problem in Nonholonomic Mechanics, Dokl. Akad. Nauk, 2008 (in press).

Borisov, A.V. and Mamaev I.S., Isomorphism and Hamilton Representation of Some Nonholonomic Systems, Siberian Math. J., 2007, vol. 48, no. 1, pp. 26–36 [Sibirsk. Mat. Zh., 2007, vol. 48, no. 1, pp. 33–45]; arxiv.org/pdf/nlin.SI/0509036.

Marikhin, V.G. and Sokolov, V.V., Pairs of Commuting Hamiltonians that are Quadratic in Momenta, Theoret. and Math. Phys., 2006, vol. 149, no. 2, pp. 1425–1436 [Teoret. Mat. Fiz., 2006, vol. 149, no. 2, pp. 147–160].

Eisenhart, L.P., Separable Systems of Stäckel, Annals of Mathematics, 1934, vol. 35, no. 2, pp. 284–305.

Ehlers, K. and Koiller, J., Rubber Rolling over a Sphere, Regul. Chaotic Dyn., 2007, vol. 12, no. 2, pp. 127–152.

Braden, H.W., A Completely Integrable Mechanical System, Lett. in Math. Phys., 1982, vol. 6, pp. 449–452.

Poincaré, H., On Curves Defined by Differential Equations, Moscow-Leningrad: Gostekhizdat, 1947.

Routh, E., Dynamics of a System of Rigid Bodies. Part II, New York: Dover Publications, 1905.

Markeev, A.P., On the Dynamics of a Top, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 1986, no. 3, pp. 30–38 (in Russian).

Karapetyan, A.V., On the Realization of Non-holonomic Constraints by Forces of Viscous Friction and the Stability of Celtic Stones, J. Appl. Math. Mech., 1982, vol. 45, pp. 30–36 [Prikl. Mat. Mekh., 1981, vol. 45, pp. 42–51].

Moshchuk, N.K., On the Motion of the Chaplygin Ball on a Hotisontal Plane, Prikl. Mat. Mekh., 1983, vol. 47, no. 6, pp. 916–921.

Moshchuk, N.K., Qualitative Analysis of the Motion of a Rigid Body of Revolution on an Absolutely Rough Plane, J. Appl. Math. Mech., 1988, vol. 52, no. 2, pp. 159–165 [Prikl. Mat. Mekh., 1988, vol. 52, no. 2, pp. 203–210].

Jensen, E.T. and Shegelski, M.R.A., The Motion of Curling Rocks: Experimental Investigation and Semi-Phenomenological Description, Can. J. Phys./Rev. Can. Phys., 2004, vol. 82, no. 10, pp. 791–809.

Persson, B.N.J., Sliding Friction — Physical Principals and Applications, 2nd ed., London: Springer, 2000.

Neimark, Yu.I. and Fufaev, N.A., Dynamics of Nonholonomic Systems, vol. 33 of Trans. of Math. Mon., 1972.

Erismann, Th., Theorie und Anwendungen des echten Kugelgetriebes, Z. angew. Math. Phys., 1954, vol. 5, pp. 355–388.

Zhuravlev, V.F., On a Model of Dry Friction in the Problem of the Rolling of Rigid Bodies, J. Appl. Math. Mech., 1998, vol. 62, no. 5, pp. 705–710 [Prikl. Mat. Mekh., 1998, vol. 62, no. 5, pp. 762–767].

Zhuravlev, V.F., Dynamics of a Heavy Homogeneous Body on a Rough Plane, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 2006, no. 6, pp. 3–8 (in Russian).

Zhuravlev, V.F. and Klimov, D.M., Global Motion of a Rattleback, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 2008, no. 3, pp. 8–16 (in Russian).

Leine, R.I., Le Saux, C., and Glocker, C., Friction Models for the Rolling Disk, ENOC-2005, Eindhoven, Netherlands, August, 2005.

Kozlov, V.V., Realization of Nonintegrable Constraints in Classical Mechanics, Soviet Phys. Dokl., 1983, vol. 28, no. 9, pp. 735–737 [Dokl. Akad. Nauk SSSR, 1983, vol. 272, no. 3, pp. 550–554].

Argatov, I.I., Equilibrium conditions for a rigid body on a rough plane in the case of axially symmetric distribution of normal pressures, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 2005, no. 2, pp. 16–26 (in Russian).

Farkas, Z., Bartels, G., Unger, T., and Wolf, D.E., Frictional Coupling between Sliding and Spinning Motion, Phys. Rev. Let., 2003, vol. 90, no. 24, 248302 (4 pages).

Zhuravlev, V.F. and Klimov, D.M., On the Dynamics of the Thompson Top (Tippe Top) on a Plane with Real Dry Friction, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 2005, no. 6, pp. 157–168 (in Russian).

Pfeiffer, F., Einführung in die Dynamik (Introduction to dynamics), Teubner Studienbücher Mechanik [Teubner Mechanics Textbooks], Stuttgart: B.G. Teubner, 1989.

Jellet, J.H., A Treatise on the Theory of Friction, London: Macmillan, 1872.

Markeev, A.P., Dinamika tela, soprikasayushchegosya s tverdoi poverkhnost’yu (The Dynamics of a Body Contiguous to a Solid Surface), Moscow: Nauka, 1991.

Kozlov, V.V. and Kolesnikov, N.N., On Theorems of Dynamics, J. Appl. Math. Mech., 1978, vol. 42, no. 1, pp. 28–33 (in Russian).

Borisov, A.V. and Mamaev, I.S., An Integrable System with a Nonintegrable Constraint, Math. Notes, 2006, vol. 80, no. 1–2, pp. 127–130 [Mat. Zametki, 2006, vol. 80, no. 1, pp. 131–134].

Kessler, P. and O’Reilly, O.M., The Ringing of Euler’s Disk, Regul. Chaotic Dyn., 2002, vol. 7, pp. 49–60.

Appell, P., Traité de mécanique rationelle, Paris: Gauthier-Villars, 1896.

Coriolis, G., Théorie mathématique des effects du jeu de Billard, Paris: Carilian-Goeury, 1835.

Ivanov, A.P., On Detachment Conditions in the Problem on the Motion of a Rigid Body on a Rough Plane, Regul. Chaotic Dyn., 2008, vol. 13, no. 4, pp. 355–368.

Ivanov, A.P., Geometric Representation of Detachment Conditions in a System with Unilateral Constraint, Regul. Chaotic Dyn., 2008, vol. 13, no. 5, pp. 436–443.

Fedorov, Yu.N., New Cases of the Integrability of the Equations of Motion of a Rigid Body in the Presence of a Nonholonomic Constraint, in Geometry, Differential Equations and Mechanics, Moscow: Moskov. Gos. Univ., Mekh.-Mat. Fak., 1986, pp. 151–155.

Kotter, F., Ueber die Bewegung eines festen Korpers in einer Flussigkeit, Z. angew. Math. Phys., 1892, vol. 109, Part I: pp. 51–81, Part II: pp. 89–111.

Sokolov, V.V. and Marikhin, V.G., Separation of Variables on a Non-hyperelliptic Curve, Regul. Chaotic Dyn., 2005, vol. 10, pp. 59–70.

Marikhin, V.G. and Sokolov, V.V., On the Reduction of the Pair of Hamiltonians Quadratic in Momenta to Canonic Form and Real Partial Separation of Variables for the Clebsch Top, Rus. J. Nonlin. Dyn., 2008, vol. 4, no. 3 (in press).

Fedorov, Yu.N., The Motion of a Rigid Body in a Spherical Support, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1988, no. 5, pp. 91–93 (in Russian).

Kharlamov, A.P., Topologicheskii analiz integriruemykh zadach dinamiki tverdogo tela (Topological Analysis of Integrable Problems of Rigid Body Dynamics), Leningrad. Univ., 1988.

Fedorov, Yu.N., Dynamic Systems with the Invariant Measure on Riemann’s Symmetric Pairs (gl(n), so(n)), Regul. Chaotic Dyn., 1996, vol. 1, no. 1, pp. 38–44.

Fedorov, Yu.N. and Jovanović, B., Quasi-Chaplygin Systems and Nonholonomic Rigid Body Dynamics, Lett. Math. Phys., 2006, vol. 76, pp. 215–230.

Fedorov, Yu.N. and Kozlov, V.V., Various Aspects of n-Dimensional Rigid Body Dynamics, vol. 168 of Amer. Math. Soc. Transl. (2), 1995, pp. 141–171.

Moiseev, N.N. and Rumyantsev, V.V., Dinamika tela s polostyami, soderzhaschimi zhidkost’ (Dynamics of a Body with Cavities Filled with Liquid), Moscow: Nauka, 1965.

Karapetyan, A.V. and Prokonina, O.V., On the Stability of Uniform Rotations of a Top with a Fluid-Filled Cavity on a Plane with Friction, J. Appl. Math. Mech., 2000, vol. 64, no. 1, pp. 81–86 [Prikl. Mat. Mekh., 2000, vol. 64, no. 1, pp. 85–91].