Authors: Dragović, Vladimir 
Gajić, Borislav 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Points with rotational ellipsoids of inertia, envelopes of hyperplanes which equally fit the system of points in Rk, and ellipsoidal billiards
Journal: Physica D: Nonlinear Phenomena
First page: 133776
Issue Date: 2023
Rank: ~M21a
ISSN: 0167-2789
DOI: 10.1016/j.physd.2023.133776
For a given system of material points in Rk which represents a sample of a full rank, we study the points for which the ellipsoid of inertia is rotational. Using an initial information about such points with a rotational ellipsoid of inertia along the line of the major axis of the central ellipsoid of inertia, we construct a pencil of confocal quadrics with the following property: all the hyperplanes for which the hyperplanar moments of inertia for the given system of points are equal, are tangent to one of the quadrics from the pencil of quadrics. We close the loop by applying the confocal pencil of quadrics to get a full description of the points with rotational hyperplanar ellipsoids of inertia. We indicate relationships of the obtained results with integrable billiards within quadrics and PCA.
Keywords: Billiards within quadrics | Confocal pencil of quadrics | Hyper-planar moments of inertia
Publisher: Elsevier

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