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.
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.
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
\Bibitem{BorKilMam15}
\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 37 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)
I. A. Bizyaev, E. V. Vetchanin, “Climb of the Chaplygin Sleigh on an Inclined Plane under Periodic Controls: Speedup and Uniform Motion”, Rus. J. Nonlin. Dyn., 20:4 (2024), 463–479
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
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
Evgeniya Mikishanina, “The problem of acceleration in the dynamics of a double-link wheeled vehicle with arbitrarily directed periodic excitation”, Theor. Appl. Mech., 50:2 (2023), 205–221
E. A. Mikishanina, “Negolonomnye mekhanicheskie sistemy na ploskosti s peremennym uglom naklona”, Zhurnal SVMO, 25:4 (2023), 326–341
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
Mate Antali, “Bifurcations of the limit directions in extended Filippov systems”, Physica D: Nonlinear Phenomena, 445 (2023), 133622
E. M. Artemova, A. A. Kilin, “A Nonholonomic Model and Complete Controllability
of a Three-Link Wheeled Snake Robot”, Rus. J. Nonlin. Dyn., 18:4 (2022), 681–707
E. A. Mikishanina, “Dynamics of a Controlled Articulated n-trailer
Wheeled Vehicle”, Rus. J. Nonlin. Dyn., 17:1 (2021), 39–48
Bizyaev I. Bolotin S. Mamaev I., “Normal Forms and Averaging in An Acceleration Problem in Nonholonomic Mechanics”, Chaos, 31:1 (2021), 013132
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
Kirill S. Yefremov, Tatiana B. Ivanova, Alexander A. Kilin, Yury L. Karavaev, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
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
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dynamics of a Chaplygin sleigh with an unbalanced rotor: regular and chaotic motions”, Nonlinear Dyn., 98:3 (2019), 2277–2291
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
M. Antali, G. Stepan, “Nonsmooth analysis of three-dimensional slipping and rolling in the presence of dry friction”, Nonlinear Dyn., 97:3, SI (2019), 1799–1817
A. Borisov, A. Kilin, I. Mamaev, “Invariant submanifolds of genus 5 and a Cantor staircase in the nonholonomic model of a snakeboard”, Int. J. Bifurcation Chaos, 29:3 (2019), 1930008
I. A. Bizyaev, A. V. Borisov, S. P. Kuznetsov, “The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass”, Nonlinear Dyn., 95:1 (2019), 699–714
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