A. V. Borisov, A. A. Kilin, I. S. Mamaev, “On the Hadamard–Hamel problem and the dynamics of wheeled vehicles”, Nelin. Dinam., 12:1 (2016), 145–163; Regul. Chaotic Dyn., 20:6 (2015), 752

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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2016, Volume 12, Number 1, Pages 145–163 (Mi nd517)

This article is cited in 32 scientific papers (total in 32 papers)

Translated papers

On the Hadamard–Hamel problem and the dynamics of wheeled vehicles

A. V. Borisov^a, A. A. Kilin^b, I. S. Mamaev^a

^a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
^b Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia

Full-text PDF (445 kB) Citations (32)

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Abstract: In this paper, we develop the results obtained by J.Hadamard and G.Hamel concerning the possibility of substituting nonholonomic constraints into the Lagrangian of the system without changing the form of the equations of motion. We formulate the conditions for correctness of such a substitution for a particular case of nonholonomic systems in the simplest and universal form. These conditions are presented in terms of both generalized velocities and quasi-velocities. We also discuss the derivation and reduction of the equations of motion of an arbitrary wheeled vehicle. In particular, we prove the equivalence (up to additional quadratures) of problems of an arbitrary wheeled vehicle and an analogous vehicle whose wheels have been replaced with skates. As examples, we consider the problems of a one-wheeled vehicle and a wheeled vehicle with two rotating wheel pairs.

Keywords: nonholonomic constraint, wheeled vehicle, reduction, equations of motion.

Funding agency	Grant number
Russian Foundation for Basic Research	15-38-20879 мол_а_вед 15-08-09261-а

Received: 12.10.2015
Revised: 09.11.2015

English version:
Regul. Chaotic Dyn., 2015, Volume 20, Issue 6, Pages 752–766
DOI: https://doi.org/10.1134/S1560354715060106

Bibliographic databases:

Document Type: Article

UDC: 531.3

MSC: 37J60, 37N05

Language: Russian

Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “On the Hadamard–Hamel problem and the dynamics of wheeled vehicles”, Nelin. Dinam., 12:1 (2016), 145–163; Regul. Chaotic Dyn., 20:6 (2015), 752–766

Citation in format AMSBIB

\Bibitem{BorKilMam16}

\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev

\paper On the Hadamard–Hamel problem and the dynamics of wheeled vehicles

\jour Nelin. Dinam.

\yr 2016

\vol 12

\issue 1

\pages 145--163

\mathnet{http://mi.mathnet.ru/nd517}

\transl

\jour Regul. Chaotic Dyn.

\yr 2015

\vol 20

\issue 6

\pages 752--766

\crossref{https://doi.org/10.1134/S1560354715060106}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84948952940}

Linking options:

https://www.mathnet.ru/eng/nd517

https://www.mathnet.ru/eng/nd/v12/i1/p145

Translation

On the Hadamard–Hamel Problem and the Dynamics of Wheeled Vehicles
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
Regul. Chaotic Dyn., 2015, 20:6, 752–766

This publication is cited in the following 32 articles:

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
Luis C. García-Naranjo, Juan C. Marrero, David Martín de Diego, Paolo E. Petit Valdés, “Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation”, J Nonlinear Sci, 34:6 (2024)
S. N. Buryan, “«Paradoksalnyi» mekhanizm P. L. Chebysheva”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 24:4 (2024), 536–551
A. A. Ardentov, E. M. Artemova, “Abnormal extremals in the sub-Riemannian problem for a general model of a robot with a trailer”, Sb. Math., 214:10 (2023), 1351–1372
Ivan A. Bizyaev, Ivan S. Mamaev, “Roller Racer with Varying Gyrostatic Momentum: Acceleration Criterion and Strange Attractors”, Regul. Chaotic Dyn., 28:1 (2023), 107–130
E. A. Mikishanina, “Nonholonomic mechanical systems on a plane with a variable slope”, Zhurnal SVMO, 25:4 (2023), 326–341
Mate Antali, “Bifurcations of the limit directions in extended Filippov systems”, Physica D: Nonlinear Phenomena, 445 (2023), 133622
Evgeniya Mikishanina, “The problem of acceleration in the dynamics of a double-link wheeled vehicle with arbitrarily directed periodic excitation”, Theor appl mech (Belgr), 50:2 (2023), 205
E. M. Artemova, A. A. Kilin, Yu. V. Korobeinikova, “Issledovanie orbitalnoi ustoichivosti pryamolineinykh kachenii roller-reisera po vibriruyuschei ploskosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:4 (2022), 615–629
Ivan Bizyaev, Sergey Bolotin, Ivan Mamaev, “Normal forms and averaging in an acceleration problem in nonholonomic mechanics”, Chaos, 31:1 (2021), 13132–28
Kirill S. Yefremov, Tatiana B. Ivanova, Alexander A. Kilin, Yury L. Karavaev, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
A. V. Borisov, E. A. Mikishanina, S. V. Sokolov, “Dynamics of Multi-Link Uncontrolled Wheeled Vehicle”, Russ. J. Math. Phys., 27:4 (2020), 433–445
Ivan A. Bizyaev, Alexey V. Borisov, Sergey P. Kuznetsov, “The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass”, Nonlinear Dyn, 95:1 (2019), 699
Mate Antali, Gabor Stepan, “Nonsmooth analysis of three-dimensional slipping and rolling in the presence of dry friction”, Nonlinear Dyn, 97:3 (2019), 1799
Alexey Borisov, Alexander Kilin, Ivan Mamaev, “Invariant Submanifolds of Genus 5 and a Cantor Staircase in the Nonholonomic Model of a Snakeboard”, Int. J. Bifurcation Chaos, 29:03 (2019), 1930008
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Dynamics of a Chaplygin sleigh with an unbalanced rotor: regular and chaotic motions”, Nonlinear Dyn, 98:3 (2019), 2277
I. A. Bizyaev, A. V. Borisov, V. V. Kozlov, I. S. Mamaev, “Fermi-like acceleration and power-law energy growth in nonholonomic systems”, Nonlinearity, 32:9 (2019), 3209–3233
Andrey A. Ardentov, Yury L. Karavaev, Kirill S. Yefremov, “Euler Elasticas for Optimal Control of the Motion of Mobile Wheeled Robots: the Problem of Experimental Realization”, Regul. Chaotic Dyn., 24:3 (2019), 312–328
Oleg Kirillov, “Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles”, Entropy, 20:7 (2018), 502
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control”, Regul. Chaotic Dyn., 23:7 (2018), 983–994

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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