New integrable problems in the dynamics of particle and rigid body

被引：20

作者：

Elmandouh, A. A. ^{[1
,2
]}

机构：

[1] King Faisal Univ, Fac Sci, Dept Math & Stat, Al Ahsaa 31982, Saudi Arabia

[2] Mansoura Univ, Dept Math, Fac Sci, Mansoura 35516, Egypt

来源：

ACTA MECHANICA | 2015年 / 226卷 / 11期

关键词：

CONSERVATIVE MECHANICAL SYSTEMS; POTENTIALS; INVARIANTS; FREEDOM; S(2);

D O I：

10.1007/s00707-015-1408-1

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

In the present article, a new two-dimensional integrable system containing 17 free parameters is introduced. For giving certain values for these parameters, new integrable problems can be constructed, which generalize some known previous problems, and in some cases, we can restore some previous integrable problems. Two new integrable problems are announced, describing the motion in an Euclidean plane and on a pseudo-sphere. In the irreversible case, a new integrable problem in rigid body dynamics, which generalizes Goriachev-Chaplygin's case (Varshav Univ Izvest 3:1-13, 1916), Yehia's case (Mech Res Commun 23:423-427, 1996) and Elmandouh's case (Acta Mech 226:2461-2472, 2015), is announced.

引用

页码：3749 / 3762

页数：14