Abstract:
In this paper we discuss conditions for the existence of the Jacobi integral (that generalizes
energy) in systems with inhomogeneous and nonholonomic constraints. As an example, we
consider in detail the problem of motion of the Chaplygin sleigh on a rotating plane and the
motion of a dynamically symmetric ball on a uniformly rotating surface. In addition, we discuss
illustrative mechanical models based on the motion of a homogeneous ball on a rotating table
and on the Beltrami surface.
Citation:
A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “The Jacobi integral in nonholonomic mechanics”, Nelin. Dinam., 11:2 (2015), 377–396; Regul. Chaotic Dyn., 20:3 (2015), 383–400
This publication is cited in the following 37 articles:
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
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
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)
Alexander A. Kilin, Elena N. Pivovarova, Tatiana B. Ivanova, “Rolling of a Homogeneous Ball on a Moving Cylinder”, Regul. Chaot. Dyn., 2024
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
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)
Alexander A. Kilin, Elena N. Pivovarova, “A Particular Integrable Case in the Nonautonomous Problem
of a Chaplygin Sphere Rolling on a Vibrating Plane”, Regul. Chaotic Dyn., 26:6 (2021), 775–786
Tatiana B. Ivanova, “Non‐holonomic rolling of a ball on the surface of a rotating cylinder”, Z Angew Math Mech, 100:12 (2020)
Alexey V. Borisov, Tatiana B. Ivanova, Alexander A. Kilin, Ivan S. Mamaev, “Circular orbits of a ball on a rotating conical turntable”, Acta Mech, 231:3 (2020), 1021
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem”, Regul. Chaotic Dyn., 24:5 (2019), 560–582
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “A Parabolic Chaplygin Pendulum and a Paul Trap: Nonintegrability, Stability, and Boundedness”, Regul. Chaotic Dyn., 24:3 (2019), 329–352
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
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Comment on “Confining rigid balls by mimicking quadrupole ion trapping” [Am. J. Phys. 85, 821 (2017)]”, American Journal of Physics, 87:11 (2019), 935
Alexey V. Borisov, Tatiana B. Ivanova, Alexander A. Kilin, Ivan S. Mamaev, “Nonholonomic rolling of a ball on the surface of a rotating cone”, Nonlinear Dyn, 97:2 (2019), 1635
Vitaliy Fedonyuk, Phanindra Tallapragada, “Sinusoidal control and limit cycle analysis of the dissipative Chaplygin sleigh”, Nonlinear Dyn, 93:2 (2018), 835
Alexander A. Kilin, Elena N. Pivovarova, “Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 23:7 (2018), 887–907
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “A Nonholonomic Model of the Paul Trap”, Regul. Chaotic Dyn., 23:3 (2018), 339–354
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
Francesco Fassò, Luis C García-Naranjo, Nicola Sansonetto, “Moving energies as first integrals of nonholonomic systems with affine constraints”, Nonlinearity, 31:3 (2018), 755
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “An Invariant Measure and the Probability of a Fall in the Problem of an Inhomogeneous Disk Rolling on a Plane”, Regul. Chaotic Dyn., 23:6 (2018), 665–684
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