|
This article is cited in 10 scientific papers (total in 10 papers)
Invariant Measures of Modified $\mathrm{LR}$ and $\mathrm{L+R}$ Systems
Božidar Jovanović Mathematical Institute SANU,
Kneza Mihaila 36, 11000, Belgrade, Serbia
Abstract:
We introduce a class of dynamical systems having an invariant measure, the modifications of well-known systems on Lie groups: $\mathrm{LR}$ and $\mathrm{L+R}$ systems. As an example, we study a modified Veselova nonholonomic rigid body problem, considered as a dynamical system on the product of the Lie algebra $so(n)$ with the Stiefel variety $V_{n, r}$, as well as the associated $\epsilon\mathrm{L+R}$ system on $so(n) \times V_{n, r}$. In the $3$-dimensional case, these systems model the nonholonomic problems of motion of a ball and a rubber ball over a fixed sphere.
Keywords:
nonholonomic constraints, invariant measure, Chaplygin ball.
Received: 28.06.2015
Citation:
Božidar Jovanović, “Invariant Measures of Modified $\mathrm{LR}$ and $\mathrm{L+R}$ Systems”, Regul. Chaotic Dyn., 20:5 (2015), 542–552
Linking options:
https://www.mathnet.ru/eng/rcd20 https://www.mathnet.ru/eng/rcd/v20/i5/p542
|
Statistics & downloads: |
Abstract page: | 158 | References: | 30 |
|