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Regul. Chaotic Dyn., 2015, Volume 20, Issue 6, Pages 752–766 (Mi rcd34)  

This article is cited in 16 scientific papers (total in 16 papers)

On the Hadamard–Hamel Problem and the Dynamics of Wheeled Vehicles

Alexey V. Borisova, Alexander A. Kilinb, Ivan S. Mamaevc

a Moscow Institute of Physics and Technology, Dolgoprudnyi, 141700, Russia
b Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia
c Steklov Mathematical Institute, ul. Gubkina 8, Moscow, 119991, Russia

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
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 15-38-20879 mol_a_ved
The work of A.V.Borisov was carried out within the framework of the state assignment for institutions of higher education. The work of A.A.Kilin was supported by the RFBR grant no. 15-38-20879 mol_a_ved. The work of I.S.Mamaev was supported by the RFBR grant no. 13-01-12462-ofi_m.


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MSC: 37J60, 37N05
Received: 12.10.2015

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

Citation in format AMSBIB
\by Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper On the Hadamard--Hamel Problem and the Dynamics of Wheeled Vehicles
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 6
\pages 752--766

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    This publication is cited in the following articles:
    1. Andrey A. Ardentov, “Controlling of a Mobile Robot with a Trailer and Its Nilpotent Approximation”, Regul. Chaotic Dyn., 21:7-8 (2016), 775–791  mathnet  crossref
    2. Alexey V. Borisov, Sergey P. Kuznetsov, “Regular and Chaotic Motions of a Chaplygin Sleigh under Periodic Pulsed Torque Impacts”, Regul. Chaotic Dyn., 21:7-8 (2016), 792–803  mathnet  crossref
    3. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Historical and critical review of the development of nonholonomic mechanics: the classical period”, Regular and Chaotic Dynamics, 21:4 (2016), 455–476  mathnet  crossref  crossref  zmath  elib
    4. T. B. Ivanova, N. N. Erdakova, Yu. L. Karavaev, “Experimental investigation of the dynamics of a brake shoe”, Dokl. Phys., 61:12 (2016), 611–614  crossref  isi  scopus
    5. Ivan A. Bizyaev, “The Inertial Motion of a Roller Racer”, Regul. Chaotic Dyn., 22:3 (2017), 239–247  mathnet  crossref  mathscinet
    6. A. V. Borisov, I. S. Mamaev, “Neodnorodnye sani Chaplygina”, Nelineinaya dinam., 13:4 (2017), 625–639  mathnet  crossref  mathscinet  elib
    7. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. I. A. Bizyaev, “Sani Chaplygina s dvizhuscheisya tochechnoi massoi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 583–589  mathnet  crossref  elib
    9. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975  mathnet  crossref
    10. I. A. Bizyaev, A. V. Borisov, S. P. Kuznetsov, “Chaplygin sleigh with periodically oscillating internal mass”, EPL, 119:6 (2017), 60008  crossref  isi
    11. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Hamilton's Principle and the Rolling Motion of a Symmetric Ball”, Dokl. Phys., 62:6 (2017), 314–317  mathnet  crossref  mathscinet  isi  scopus
    12. Alexey V. Borisov, Ivan S. Mamaev, “An Inhomogeneous Chaplygin Sleigh”, Regul. Chaotic Dyn., 22:4 (2017), 435–447  mathnet  crossref  mathscinet
    13. O. N. Kirillov, “Locating the sets of exceptional points in dissipative systems and the self-stability of bicycles”, Entropy, 20:7 (2018), 502  crossref  isi  scopus
    14. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control”, Regul. Chaotic Dyn., 23:7-8 (2018), 983–994  mathnet  crossref
    15. A. A. Kilin, E. N. Pivovarova, “Chaplygin top with a periodic gyrostatic moment”, Russ. J. Math. Phys., 25:4 (2018), 509–524  crossref  mathscinet  zmath  isi  scopus
    16. 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  mathnet  crossref
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