Chaplygin ball over a fixed sphere: an explicit integration

А. В. Борисов, Yu. N. Fedorov, И. С. Мамаев

Type: Article

Publication Date: 2008-12-01

Citations: 59

DOI: https://doi.org/10.1134/s1560354708060063

View Publication

Download PDF

Locations

Regular and Chaotic Dynamics - View
arXiv (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	On the Lie integrability theorem for the Chaplygin ball	2014	A. V. Tsiganov
+	Numerical Integration on the Sphere	2010	Kerstin Hesse Ian H. Sloan Robert S. Womersley
+	Numerical Integration on the Sphere	2015	Kerstin Hesse Ian H. Sloan Robert S. Womersley
+	Numerical Integration on the Sphere	2013	Kerstin Hesse Ian H. Sloan Robert S. Womersley
+	Numerical Integration on the Sphere	2015	Kerstin Hesse Ian H. Sloan Robert S. Womersley
+ PDF Chat	Numerical Integration Over a Sphere	1968	Christopher A. Feuchter
+	Numerical Integration over Spheres of Arbitrary Dimension	2006	Johann S. Brauchart Kerstin Hesse
+	A Cauchy-Green formula on the unit sphere in 𝐶²	2003	John T. Anderson John Wermer
+	Numerical integration with polynomial exactness over a spherical cap	2011	Kerstin Hesse Robert S. Womersley
+	Quadrature over the sphere.	2005	Kendall Atkinson Alvise Sommariva
+ PDF Chat	Hamiltonization and Integrability of the Chaplygin Sphere in ℝ n	2010	Božidar Jovanović
+	Boundedness of bouncing balls in quadratic potentials	2024	Zhichao Ma Jin‐Tung Liang Junxiang Xu
+ PDF Chat	On the Poisson structures for the Chaplygin ball and its generalizations	2012	A. V. Tsiganov
+ PDF Chat	Generalized Chaplygin’s transformation and explicit integration of a system with a spherical support	2011	А. В. Борисов Alexander A. Kilin И. С. Мамаев
+	Clifford Analysis on the Sphere	1998	P. Van Lancker
+	Local numerical integration on the sphere	2014	Judith Beckmann H. N. Mhaskar Jürgen Prestin
+	Generalized Chaplygin’s transformation and explicit integration of a system with a spherical support	2012	А. В. Борисов Alexander A. Kilin И. С. Мамаев
+	The Octonionic Bergman Kernel for the Unit Ball	2018	Jinxun Wang Xingmin Li
+	A Quadrature on a Sphere: 11159.	2007	George Lamb J Grzesik
+	Tchakaloff-like compression of QMC volume and surface integration on the union of balls	2024	Giacomo Elefante Alvise Sommariva Michelangelo Vianello

Works That Cite This (33)

Action	Title	Year	Authors
+	Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges	2018	Alexander A. Kilin Elena N. Pivovarova
+	Two non-holonomic integrable problems tracing back to Chaplygin	2012	А. В. Борисов И. С. Мамаев
+	The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere	2013	А. В. Борисов И. С. Мамаев Ivan A. Bizyaev
+	Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds	2011	Alexey V. Bolsinov А. В. Борисов И. С. Мамаев
+	Geometrisation of Chaplygin's reducing multiplier theorem	2014	Alexey V. Bolsinov А. В. Борисов И. С. Мамаев
+ PDF Chat	Invariant measures of modified LR and L+R systems	2015	Božidar Jovanović
+ PDF Chat	Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere	2019	Borislav Gajić Božidar Jovanović
+	Topological analysis of an integrable system related to the rolling of a ball on a sphere	2013	А. В. Борисов И. С. Мамаев
+	An Invariant Measure and the Probability of a Fall in the Problem of an Inhomogeneous Disk Rolling on a Plane	2018	Ivan A. Bizyaev А. В. Борисов И. С. Мамаев
+ PDF Chat	Topological analysis of one integrable system related to the rolling of a ball over a sphere	2012	А. В. Борисов И. С. Мамаев

Works Cited by This (13)

Action	Title	Year	Authors
+	On the Integration Theory of Equations of Nonholonomic Mechanics	2005	В. В. Козлов
+ PDF Chat	Theta Functions on Riemann Surfaces	1973	John D. Fay
+	Chaplygin's sphere	2004	J. J. Duistermaat
+	Hyperelliptic Kleinian functions and applications	1997	Victor Matveevich Buchstaber V. Z. Enolski Дмитрий Викторович Лейкин
+	The Rolling Body Motion Of a Rigid Body on a Plane and a Sphere. Hierarchy of Dynamics	2003	А. В. Борисов И. С. Мамаев
+	Geometry of Quadrics and Spectral Theory	1980	J. Moser
+	Rolling of a non-homogeneous ball over a sphere without slipping and twisting	2007	А. В. Борисов И. С. Мамаев
+ PDF Chat	Theta functions and non-linear equations	1981	Boris Dubrovin
+	None	1999	Yu. N. Fedorov
+ PDF Chat	A Discretization of the Nonholonomic Chaplygin Sphere Problem	2007	Yuri N. Fedorov