Abstract:
This paper is a review of the problem of the constructive reduction of nonholonomic systems with symmetries. The connection of reduction with the presence of the simplest tensor invariants (first integrals and symmetry fields) is shown. All theoretical constructions are illustrated by examples encountered in applications. In addition, the paper contains a short historical and critical sketch covering the contribution of various researchers to this problem.
Sections 2-4 were written by A. V. Borisov and supported by the RSF grant no. 15-12-20035. Sections 5, 6 and Appendices were written by I. S. Mamaev within the framework of the RSF grant no. 14-19-01303.
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A. G. Agúndez, D. García-Vallejo, E. Freire, “Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints”, Nonlinear Dyn, 112:4 (2024), 2453
S. X. Jin, Y. M. Li, X. W. Chen, “Noether theorem and its inverse for nonstandard generalized Chaplygin systems”, Acta Mech, 235:2 (2024), 1361
E.M. Artemova, I.A. Bizyaev, “Dynamics of a multilink wheeled vehicle: Partial solutions and unbounded speedup”, International Journal of Non-Linear Mechanics, 165 (2024), 104774
Ivan A. Bizyaev, Ivan S. Mamaev, “Nonlinear Dynamics of a Roller Bicycle”, Regul. Chaotic Dyn., 29:5 (2024), 728–750
Jorge S. Garcia, Tomoki Ohsawa, “Controlled Lagrangians and Stabilization of Euler–Poincaré Equations with Symmetry Breaking Nonholonomic Constraints”, J Nonlinear Sci, 34:5 (2024)
Ivan A. Bizyaev, Ivan S. Mamaev, “Roller Racer with Varying Gyrostatic Momentum:
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A. A. Kilin, T. B. Ivanova, “The Integrable Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint”, Rus. J. Nonlin. Dyn., 19:1 (2023), 3–17
A. A. Kilin, T. B. Ivanova, “The Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint”, Rus. J. Nonlin. Dyn., 19:4 (2023), 533–543
Evgeniya A. Mikishanina, “Dynamics of the generalized penny-model on the rotating plane”, Eur. Phys. J. B, 96 (2023), 15–8
Elizaveta M. Artemova, Evgeny V. Vetchanin, “The Motion of an Unbalanced Circular Disk
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Anton V. Doroshin, “Schemes of momentum/reaction wheels unloading by mechanical restructuring and gearbox for spacecraft”, Communications in Nonlinear Science and Numerical Simulation, 108 (2022), 106252
Paula Balseiro, Nicola Sansonetto, “First Integrals and Symmetries of Nonholonomic Systems”, Arch Rational Mech Anal, 244:2 (2022), 343
J. Xiong, Y.-B. Jia, C. Liu, “Symmetry and Relative Equilibria of a Bicycle System”, Rus. J. Nonlin. Dyn., 17:4 (2021), 391–411
Mamaev I.S. Bizyaev I.A., “Dynamics of An Unbalanced Circular Foil and Point Vortices in An Ideal Fluid”, Phys. Fluids, 33:8 (2021), 087119
Popescu M., Popescu P., “Noether Invariants For Nonholonomic Systems”, Symmetry-Basel, 13:4 (2021), 641
Kilin A.A. Pivovarova E.N., “The Influence of the First Integrals and the Rolling Resistance Model on Tippe TOP Inversion”, Nonlinear Dyn., 103:1 (2021), 419–428
V. Gzenda, V. Putkaradze, “Integrability and chaos in figure skating”, J. Nonlinear Sci., 30:3 (2020), 831–850
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Alexander A. Kilin, Elena N. Pivovarova, “Stability and Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base”, Regul. Chaotic Dyn., 25:6 (2020), 729–752
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