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This article is cited in 6 scientific papers (total in 6 papers)
On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff–Love Constraints
Vasyl Kovalchuk Institute of Fundamental Technological Research, Polish Academy of Sciences, 5B Pawińskiego Str., 02-106 Warsaw, Poland
Abstract:
In this article we consider the affinely-rigid body moving in the three-dimensional physical space and subject to the Kirchhoff–Love constraints, i.e., while it deforms homogeneously in the two-dimensional central plane of the body it simultaneously performs one-dimensional oscillations orthogonal to this central plane. For the polar decomposition we obtain the stationary ellipsoids as special solutions of the general, strongly nonlinear equations of motion. It is also shown that these solutions are conceptually different from those obtained earlier for the two-polar (singular value) decomposition.
Keywords:
affinely-rigid bodies with degenerate dimension; Kirchhoff–Love constraints; polar decomposition; Green deformation tensor; deformation invariants; stationary ellipsoids as special solutions.
Received: November 13, 2009; in final form March 31, 2010; Published online April 8, 2010
Citation:
Vasyl Kovalchuk, “On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff–Love Constraints”, SIGMA, 6 (2010), 031, 12 pp.
Linking options:
https://www.mathnet.ru/eng/sigma488 https://www.mathnet.ru/eng/sigma/v6/p31
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Abstract page: | 250 | Full-text PDF : | 38 | References: | 46 |
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