The upper bound of minimum moment of inertia of equi-area convex domains |
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| Authors: | Nassir Monemi Arsalan Ghahramani |
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| Institution: | Department of Civil Engineering Pahlavi University, Shiraz, Iran |
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| Abstract: | The problem of nontrivial bounds of moments of inertia for plane configurations is formulated. The Winternitz theorem is generalized to establish the bounds of the ratio of the Nth moment of areas of two subdomains created by any of the centroidal axes of a convex domain. For convex equi-area domains the upper bound of the minimum moment of inertia with respect to a general coordinate system is discussed. In particular, for the cases of the origin of coordinate axes coinciding with the centroid and coinciding with a point on the periphery, the upper bound of the minimum moment of inertia is proved to belong to an equilateral triangle and an isosceles 120° triangle, respectively. |
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