On the Model of Non-holonomic Billiard

被引：4

作者：

Borisov, Alexey V. ^{[1
]}

Kilin, Alexander A. ^{[1
]}

Mamaev, Ivan S. ^{[1
]}

机构：

[1] Udmurt State Univ, Inst Comp Sci, Izhevsk 426034, Russia

来源：

REGULAR & CHAOTIC DYNAMICS | 2011年 / 16卷 / 06期

关键词：

billiard; impact; point map; nonintegrability; periodic solution; nonholonomic constraint; integral of motion; IMPACT; BALL;

D O I：

10.1134/S1560354711060062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball. This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique, the non-integrability of the non-holonomic billiard within an ellipse is shown.

引用

页码：653 / 662

页数：10

共 25 条

[1]

[Anonymous], 1835, THEORIE MATH EFFETS

[2]

Appell P., 1911, J MATH PURES APPL 6, V7, P85

[3]

BAYES J, 1963, AM J PHYS, V3, P197

[4] ROLLING OF A BALL ON A SURFACE. NEW INTEGRALS AND HIERARCHY OF DYNAMICS [J].

Borisov, A. V. ;

Mamaev, I. S. ;

Kilin, A. A. .

REGULAR & CHAOTIC DYNAMICS, 2002, 7 (02) :201-219

[5]

Chatterjee A, 1997, THESIS CORNELL U

[6] Grip-slip behavior of a bouncing ball [J].

Cross, R .

AMERICAN JOURNAL OF PHYSICS, 2002, 70 (11) :1093-1102

[7]

Derby N., 1999, PHYS TEACH, V37, P24, DOI [10.1119/1.880156, DOI 10.1119/1.880156]

[8]

Dragovic V., 2010, INTEGRABLE BILLIARDS

[9] On frictionless impact models in rigid-body systems [J].

Glocker, C .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 359 (1789) :2385-2404

[10]

Goldsmith W., 1960, Impact: The Theory of Physical Behaviour of Colliding Solids

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