Аннотация:
We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their "gauge-like" generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution.
Образец цитирования:
Francesco Fassò, Nicola Sansonetto, “Conservation of Energy and Momenta in Nonholonomic Systems with Affine Constraints”, Regul. Chaotic Dyn., 20:4 (2015), 449–462
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\by Francesco Fass\`o, Nicola Sansonetto
\paper Conservation of Energy and Momenta in Nonholonomic Systems with Affine Constraints
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 4
\pages 449--462
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https://www.mathnet.ru/rus/rcd25
https://www.mathnet.ru/rus/rcd/v20/i4/p449
Эта публикация цитируется в следующих 23 статьяx:
Mariana Costa-Villegas, Luis C. García-Naranjo, “Affine Generalizations of the Nonholonomic Problem of a Convex Body Rolling without Slipping on the Plane”, Regul. Chaot. Dyn., 2025
Federico Talamucci, “Nonlinear nonholonomic systems: a simple approach and various examples”, Meccanica, 59:3 (2024), 333
Efstratios Stratoglou, Alexandre Anahory Simoes, Anthony Bloch, Leonardo Colombo, Lecture Notes in Computer Science, 14072, Geometric Science of Information, 2023, 89
Fabio Sozio, Arash Yavari, “A Geometric Field Theory of Dislocation Mechanics”, J Nonlinear Sci, 33:5 (2023)
Francesco Fassò, Nicola Sansonetto, “On Some Aspects of the Dynamics of a Ball in a Rotating
Surface of Revolution and of the Kasamawashi Art”, Regul. Chaotic Dyn., 27:4 (2022), 409–423
S. Hajdú, T. Mestdag, “Nonlinear splittings on fibre bundles”, Anal.Math.Phys., 12:1 (2022)
Jesus E. Pacheco-Villegas, Vicente Parra-Vega, Anand E. Sanchez-Orta, 2022 19th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), 2022, 1
Marco Dalla Via, Francesco Fassò, Nicola Sansonetto, “On the Dynamics of a Heavy Symmetric Ball that Rolls Without Sliding on a Uniformly Rotating Surface of Revolution”, J Nonlinear Sci, 32:6 (2022)
T. B. Ivanova, “Non-holonomic rolling of a ball on the surface of a rotating cylinder”, ZAMM-Z. Angew. Math. Mech., 100:12 (2020), e202000067
A. V. Tsiganov, “On a time-dependent nonholonomic oscillator”, Russ. J. Math. Phys., 27:3 (2020), 399–409
Yan Gao, 5TH INTERNATIONAL CONFERENCE ON ENERGY SCIENCE AND APPLIED TECHNOLOGY (ESAT 2019), 2238, 5TH INTERNATIONAL CONFERENCE ON ENERGY SCIENCE AND APPLIED TECHNOLOGY (ESAT 2019), 2020, 020004
F. Fasso, L. C. Garcia-Naranjo, N. Sansonetto, “Moving energies as first integrals of nonholonomic systems with affine constraints”, Nonlinearity, 31:3 (2018), 755–782
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dynamics of the Chaplygin ball on a rotating plane”, Russ. J. Math. Phys., 25:4 (2018), 423–433
B. Jovanovic, “Symmetries of line bundles and noether theorem for time-dependent nonholonomic systems”, J. Geom. Mech., 10:2 (2018), 173–187
А. В. Борисов, И. С. Мамаев, “Неоднородные сани Чаплыгина”, Нелинейная динам., 13:4 (2017), 625–639
R. Chhabra, M. R. Emami, Ya. Karshon, “Reduction of Hamiltonian mechanical systems with affine constraints: a geometric unification”, J. Comput. Nonlinear Dyn., 12:2, SI (2017), 021007
Alexey V. Borisov, Ivan S. Mamaev, “An Inhomogeneous Chaplygin Sleigh”, Regul. Chaotic Dyn., 22:4 (2017), 435–447
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Hojman Construction and Hamiltonization of Nonholonomic Systems”, SIGMA, 12 (2016), 012, 19 pp.
Yury A. Grigoryev, Alexey P. Sozonov, Andrey V. Tsiganov, “Integrability of Nonholonomic Heisenberg Type Systems”, SIGMA, 12 (2016), 112, 14 pp.
Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Spiral Chaos in the Nonholonomic Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 939–954
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