caa a22 4500 445811358 CHVBK 20180317145213.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s00419-009-0400-4 doi (NATIONALLICENCE)springer-10.1007/s00419-009-0400-4 Areal moments of inertia revisited: on the distinction between the principal directions [Elektronische Daten] [Vlado Lubarda, Yujia Liu] Three commonly used methods to determine the principal moments of inertia of a plane area and their directions are based on: (i) the stationarity condition for the axial moment of inertia, (ii) the eigenvalue analysis, and (iii) Mohr's circle. In this paper we provide two new derivations, which are based on: (a) the matrix diagonalization and the invariant tensor properties, and (b) the conjugacy property of the moment of inertia vectors. A new general expression is derived which specifies the principal directions of inertia, as well as the directions of the maximum and minimum product of inertia. A comparative study of the five presented approaches is given, which is of interest from both conceptual and methodological points of view. The connection between the deviatoric part of the moment of inertia tensor and Land's circle of inertia is also given. The presented analysis applies to any two-by-two symmetric second order tensor. The Author(s), 2009 Diagonalization nationallicence Eigenvalue analysis nationallicence Inertia vectors nationallicence Land's circle nationallicence Moment of inertia nationallicence Mohr's circle nationallicence Principal directions nationallicence Lubarda Vlado Department of Mechanical and Aerospace Engineering, University of California, San Diego, 92093-0411, La Jolla, CA, USA aut Liu Yujia Department of Mechanical and Aerospace Engineering, University of California, San Diego, 92093-0411, La Jolla, CA, USA aut Archive of Applied Mechanics Springer-Verlag 81/1(2011-01-01), 111-122 0939-1533 81:1<111 2011 81 419 https://doi.org/10.1007/s00419-009-0400-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-009-0400-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lubarda Vlado Department of Mechanical and Aerospace Engineering, University of California, San Diego, 92093-0411, La Jolla, CA, USA aut NATIONALLICENCE 700 1- Liu Yujia Department of Mechanical and Aerospace Engineering, University of California, San Diego, 92093-0411, La Jolla, CA, USA aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 81/1(2011-01-01), 111-122 0939-1533 81:1<111 2011 81 419 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer