ROLLING OF A BALL ON A SURFACE. NEW INTEGRALS AND HIERARCHY OF DYNAMICS

被引：83

作者：

Borisov, A. V. ^{[1
]}

Mamaev, I. S. ^{[2
]}

Kilin, A. A. ^{[2
]}

机构：

[1] Moscow MV Lomonosov State Univ, Dept Theoret Mech, Moscow 119899, Russia

[2] Udmurt State Univ, Lab Dynam Chaos & Nonlinear, Izhevsk 426034, Russia

来源：

REGULAR & CHAOTIC DYNAMICS | 2002年 / 7卷 / 02期

关键词：

D O I：

10.1070/RD2002v007n02ABEH000205

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper concerns the problem on the rolling of a homogeneous ball on an arbitrary surface. The new cases are presented when the problem is solved by quadratures. The paper also indicates the special case of existence of one more additional integral and invariant measure. Using this case, we obtain the nonholonomic generalization of the Jacobi problem for the inertial motion of a point on an ellipsoid. In case of a ball rolling it is also shown that on an arbitrary cylinder in the gravity field its motion is bounded and, on the average, it does not move downwards. All the results of the paper essentially expand the investigations by E. Routh, carried out in XIX century.

引用

页码：201 / 219

页数：19

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