Аннотация:
A spherical rigid body rolling without sliding on a horizontal support is considered.
The body is axially symmetric but unbalanced (tippe top). The support performs highfrequency
oscillations with small amplitude. To implement the standard averaging procedure,
we present equations of motion in quasi-coordinates in Hamiltonian form with additional terms
of nonholonomicity [16] and introduce a new fast time variable. The averaged system is similar
to the initial one with an additional term, known as vibrational potential [8, 9, 18]. This
term depends on the single variable — the nutation angle θ, and according to the work
of Chaplygin [5], the averaged system is integrable. Some examples exhibit the influence of
vibrations on the dynamics.
Образец цитирования:
Alexey V. Borisov, Alexander P. Ivanov, “A Top on a Vibrating Base:
New Integrable Problem of Nonholonomic Mechanics”, Regul. Chaotic Dyn., 27:1 (2022), 2–10
\RBibitem{BorIva22}
\by Alexey V. Borisov, Alexander P. Ivanov
\paper A Top on a Vibrating Base:
New Integrable Problem of Nonholonomic Mechanics
\jour Regul. Chaotic Dyn.
\yr 2022
\vol 27
\issue 1
\pages 2--10
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https://www.mathnet.ru/rus/rcd1148
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Эта публикация цитируется в следующих 5 статьяx:
Changji Xu, Fan Yang, Horng-Tzer Yau, Jun Yin, “Bulk universality and quantum unique ergodicity for random band matrices in high dimensions”, Ann. Probab., 52:3 (2024)
Alexander A. Kilin, Elena N. Pivovarova, “Bifurcation analysis of the problem of a “rubber” ellipsoid of revolution rolling on a plane”, Nonlinear Dyn, 2024
Alexander A. Kilin, Tatiana B. Ivanova, Elena N. Pivovarova, “Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback”, Regul. Chaotic Dyn., 28:6 (2023), 888–905
Alexander A. Kilin, Elena N. Pivovarova, “Stability of Vertical Rotations of an Axisymmetric Ellipsoid on a Vibrating Plane”, Mathematics, 11:18 (2023), 3948
Sean R. Dawson, Holger R. Dullin, Diana M.H. Nguyen, “The Harmonic Lagrange Top
and the Confluent Heun Equation”, Regul. Chaotic Dyn., 27:4 (2022), 443–459
Цитирование в формате AMSBIB
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