A Note about Torsional Rigidity and Euclidean Moment of Inertia of Plane Domains
- Authors: Salakhudinov R.G.1
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Affiliations:
- N. I. Lobachevskii Institute of Mathematics and Mechanics
- Issue: Vol 39, No 6 (2018)
- Pages: 826-834
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/202479
- DOI: https://doi.org/10.1134/S1995080218060161
- ID: 202479
Cite item
Abstract
Denote by P(G) the torsional rigidity of a simply connected plane domain G, and by I2(G) the Euclidean moment of inertia of G. In 1995 F.G. Avkhadiev proved that P(G) and I2(G) are comparable quantities in sense of Pólya and Szegö. Moreover, it was shown that the ratio P(G) /I2(G) belongs to the segment [1, 64]. We investigate the following conjecture P(G) ≥ 3I2(G), where G is a simply connected domain. We prove that the conjecture is true for polygonal domains circumscribed about a circle. For convex domains we show sharp isoperimetric inequalities, which justify the conjecture, in particular, we prove that P(G) > 2I2(G). Some aspects of approximate formulas for P(G) are also discussed.
About the authors
R. G. Salakhudinov
N. I. Lobachevskii Institute of Mathematics and Mechanics
Author for correspondence.
Email: rsalakhud@gmail.com
Russian Federation, ul. Kremlevskaya 18, Kazan, Tatarstan, 420008