New integrable problems in the dynamics of particle and rigid body

被引：0
作者：
A. A. Elmandouh
机构：
[1] King Faisal University,Department of Mathematics and Statistics, Faculty of Science
[2] Mansoura University,Department of Mathematics, Faculty of Science
来源：
Acta Mechanica | 2015年 / 226卷
关键词：
Rigid Body; Gaussian Curvature; Euclidean Plane; Integrable Problem; Point Transformation;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：3749 / 3762
页数：13
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