## Journal of Geometry and Symmetry in Physics

### Classical Models of Affinely-Rigid Bodies with “Thickness” in Degenerate Dimension

#### Abstract

The special interest is devoted to such situations when the material space of object with affine degrees of freedom has generally lower dimension than the one of the physical space. In other words when we have $m$-dimensional affinely-rigid body moving in the $n$-dimensional physical space, $m\lt n$. We mainly concentrate on the physical situation $m=2$, $n=3$ when “thickness” of flat bodies performs one-dimensional oscillations orthogonal to the two-dimensional central plane of the body. For the isotropic case in two “flat” dimensions some special solutions, namely, the stationary ellipses, which are analogous to the ellipsoidal figures of equilibrium well known in astro- and geophysics, e.g., in the theory of the Earth's shape, are obtained.

#### Article information

Source
J. Geom. Symmetry Phys., Volume 14 (2009), 51-65.

Dates
First available in Project Euclid: 24 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.jgsp/1495591239

Digital Object Identifier
doi:10.7546/jgsp-14-2009-51-65

Mathematical Reviews number (MathSciNet)
MR2536499

Zentralblatt MATH identifier
1171.70003

#### Citation

Kovalchuk, Vasyl; Rożko, Ewa Eliza. Classical Models of Affinely-Rigid Bodies with “Thickness” in Degenerate Dimension. J. Geom. Symmetry Phys. 14 (2009), 51--65. doi:10.7546/jgsp-14-2009-51-65. https://projecteuclid.org/euclid.jgsp/1495591239