Integrable Discretization and Deformation of the Nonholonomic Chaplygin Ball

被引：10
|
作者：
Tsiganov, Andrey V. [1 ]
机构：
[1] St Petersburg State Univ, Ul Ulyanovskaya 1, St Petersburg 198504, Russia
来源：
REGULAR & CHAOTIC DYNAMICS | 2017年 / 22卷 / 04期
基金：
俄罗斯科学基金会;
关键词：
nonholonomic systems; Abel quadratures; arithmetic of divisors; BACKLUND-TRANSFORMATIONS; EXPLICIT INTEGRATION; SYSTEMS; DYNAMICS; HIERARCHY; PLANE;
D O I：
10.1134/S1560354717040025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The rolling of a dynamically balanced ball on a horizontal rough table without slipping was described by Chaplygin using Abel quadratures. We discuss integrable discretizations and deformations of this nonholonomic system using the same Abel quadratures. As a by-product one gets a new geodesic flow on the unit two-dimensional sphere whose additional integrals of motion are polynomials in the momenta of fourth order.
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页码：353 / 367
页数：15
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