|
References
|
|
[1] |
Arnol'd, V. I., Kozlov, V. V., and Neĭshtadt, A. I., Mathematical Aspects of Classical and Celestial Mechanics, Encyclopaedia Math. Sci., 3, 3rd ed., Springer, Berlin, 2006, xiv+518 pp. |
[2] |
Bakša, A., “On Geometrization of Some Nonholonomic Systems”, Theor. Appl. Mech., 44:2 (2017), 133–140 ; Mat. Vesnik, 27 (1975), 233–240 (Russian) |
[3] |
Bolsinov, A. V., Borisov, A. V., and Mamaev, I. S., “Rolling of a Ball without Spinning on a Plane: The Absence of an Invariant Measure in a System with a Complete Set of Integrals”, Regul. Chaotic Dyn., 17:6 (2012), 571–579 |
[4] |
Borisov, A. V., Mamaev, I. S., and Bizyaev, I. A., “The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere”, Regul. Chaotic Dyn., 18:3 (2013), 277–328 |
[5] |
Bolsinov, A. V., Borisov, A. V., and Mamaev, I. S., “Geometrisation of Chaplygin's Reducing Multiplier Theorem”, Nonlinearity, 28:7 (2015), 2307–2318 |
[6] |
Bolsinov, A. V., “Complete Commutative Subalgebras in Polynomial Poisson Algebras: A Proof of the Mischenko – Fomenko Conjecture”, Theor. Appl. Mech., 43:2 (2016), 145–168 |
[7] |
Borisov, A. V. and Fedorov, Yu. N., “On Two Modified Integrable Problems in Dynamics”, Mosc. Univ. Mech. Bull., 50:6 (1995), 16–18 ; Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 6, 102–105 (Russian) |
[8] |
Borisov, A. V., Fedorov, Yu. N., and Mamaev, I. S., “Chaplygin Ball over a Fixed Sphere: An Explicit Integration”, Regul. Chaotic Dyn., 13:6 (2008), 557–571 |
[9] |
Borisov, A. V. and Mamaev, I. S., “Rolling of a Non-Homogeneous Ball over a Sphere without Slipping and Twisting”, Regul. Chaotic Dyn., 12:2 (2007), 153–159 |
[10] |
Borisov, A. V., Mamaev, I. S., and Treschev, D. V., “Rolling of a Rigid Body without Slipping and Spinning: Kinematics and Dynamics”, J. Appl. Nonlinear Dyn., 2:2 (2013), 161–173 |
[11] |
Braden, H. W., “A Completely Integrable Mechanical System”, Lett. Math. Phys., 6:6 (1982), 449–452 |
[12] |
Cantrijn, F., Cortés, J., de León, M., and Martín de Diego, D., “On the Geometry of Generalized Chaplygin Systems”, Math. Proc. Cambridge Philos. Soc., 132:2 (2002), 323–351 |
[13] |
Chaplygin, S. A., “On a Ball's Rolling on a Horizontal Plane”, Regul. Chaotic Dyn., 7:2 (2002), 131–148 ; Math. Sb., 24:1 (1903), 139–168 (Russian) |
[14] |
Chaplygin, S. A., “On the Theory of Motion of Nonholonomic Systems. The Reducing-Multiplier Theorem”, Regul. Chaotic Dyn., 13:4 (2008), 369–376 ; Mat. Sb., 28:2 (1912), 303–314 (Russian) |
[15] |
Davison, Ch. M., Dullin, H. R., and Bolsinov, A. V., “Geodesics on the Ellipsoid and Monodromy”, J. Geom. Phys., 57:12 (2007), 2437–2454 |
[16] |
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, Progr. Math., 232, Birkhäuser, Boston, Mass., 2005, 75–120 |
[17] |
Koiller, J. and Ehlers, K., “Rubber Rolling over a Sphere”, Regul. Chaotic Dyn., 12:2 (2007), 127–152 |
[18] |
Fassò, F., García-Naranjo, L. C., and Montaldi, J., “Integrability and Dynamics of the $n$-Dimensional Symmetric Veselova Top”, J. Nonlinear Sci., 29:3 (2019), 1205–1246 |
[19] |
Fassò, F., García-Naranjo, L. C., and Sansonetto, N., “Moving Energies As First Integrals of Nonholonomic Systems with Affine Constraints”, Nonlinearity, 31:3 (2018), 755–782 |
[20] |
Fedorov, Yu. N. and Jovanović, B., “Nonholonomic LR Systems As Generalized Chaplygin Systems with an Invariant Measure and Flows on Homogeneous Spaces”, J. Nonlinear Sci., 14:4 (2004), 341–381 |
[21] |
Fedorov, Yu. N. and Kozlov, V. V., “Various Aspects of $n$-Dimensional Rigid Body Dynamics”, Amer. Math. Soc. Transl. Ser. 2, 168 (1995), 141–171 |
[22] |
Field, M. J., “Equivariant Dynamical Systems”, Trans. Amer. Math. Soc., 259:1 (1980), 185–205 |
[23] |
Gajić, B., “The Rigid Body Dynamics: Classical and Algebro-Geometric Integration”, Zb. Rad. (Beogr.), 16(24) (2013), 5–44 |
[24] |
Gajić, B. and Jovanović, B., “Nonholonomic Connections, Time Reparametrizations, and Integrability of the Rolling Ball over a Sphere”, Nonlinearity, 32:5 (2019), 1675–1694 |
[25] |
García-Naranjo, L. C., “Generalisation of Chaplygin's Reducing Multiplier Theorem with an Application to Multi-Dimensional Nonholonomic Dynamics”, J. Phys. A, 52:20 (2019), 205203, 16 pp. |
[26] |
García-Naranjo, L. C., “Hamiltonisation, Measure Preservation and First Integrals of the Multi-Dimensional Rubber Routh Sphere”, Theor. Appl. Mech., 46:1 (2019), 65–88 |
[27] |
Jovanović, B., “Note on a Ball Rolling over a Sphere: Integrable Chaplygin System with an Invariant Measure without Chaplygin Hamiltonization”, Theor. Appl. Mech., 46:1 (2019), 97–108 |
[28] |
Jovanović, B., “Hamiltonization and Integrability of the Chaplygin Sphere in $\mathbb{R}^n$”, J. Nonlinear. Sci., 20:5 (2010), 569–593 |
[29] |
Jovanović, B., “The Jacobi – Rosochatius Problem on an Ellipsoid: The Lax Representations and Billiards”, Arch. Ration. Mech. Anal., 210:1 (2013), 101–131 |
[30] |
Jovanović, B., “Invariant Measures of Modified LR and L+R Systems”, Regul. Chaotic Dyn., 20:5 (2015), 542–552 |
[31] |
Jovanović, B., “Noether Symmetries and Integrability in Hamiltonian Time-Dependent Mechanics”, Theor. Appl. Mech., 43:2 (2016), 255–273 |
[32] |
Jovanović, B., “Symmetries of Line Bundles and Noether Theorem for Time-Dependent Nonholonomic Systems”, J. Geom. Mech., 10:2 (2018), 173–187 |
[33] |
Jovanović, B., “Rolling Balls over Spheres in $\mathbb R^n$”, Nonlinearity, 31:9 (2018), 4006–4031 |
[34] |
Koiller, J., “Reduction of Some Classical Nonholonomic Systems with Symmetry”, Arch. Rational Mech. Anal., 118:2 (1992), 113–148 |
[35] |
Moser, J., “Various Aspects of Integrable Hamiltonian Systems”, Dynamical Systems (C.I.M.E. Summer School, Bressanone, 1978), Progr. Math., 8, Birkhäuser, Boston, Mass., 1980, 233–289 |
[36] |
Stanchenko, S. V., “Non-Holonomic Chaplygin Systems”, J. Appl. Math. Mech., 53:1 (1989), 11–17 ; Prikl. Mat. Mekh., 53:1 (1989), 16–23 (Russian) |
[37] |
Tsiganov, A. V., “Integrable Euler Top and Nonholonomic Chaplygin Ball”, J. Geom. Mech., 3:3 (2011), 337–362 |
[38] |
Tsiganov, A. V., “Integrable Discretization and Deformation of the Nonholonomic Chaplygin Ball”, Regul. Chaotic Dyn., 22:4 (2017), 353–367 |
[39] |
Veselov, A. P. and Veselova, L. E., “Flows on Lie Groups with a Nonholonomic Constraint and Integrable Non-Hamiltonian Systems”, Funct. Anal. Appl., 20:5 (1986), 308–309 ; Funktsional. Anal. i Prilozhen., 20:4 (1986), 65–66 (Russian) |
[40] |
Veselov, A. P. and Veselova, L. E., “Integrable Nonholonomic Systems on Lie Groups”, Math. Notes, 44:5 (1988), 810–819 ; Mat. Zametki, 44:5 (1988), 604–619 (Russian) |