What question did this study set out to answer?

The study aims to explore the distribution of rotation matrices on the special orthogonal group SO(3) with a focus on minimizing logarithmic energy.

April 4, 2026Constructive Approximation0 citationsOpen Access

Points on SO (3) with low logarithmic energy

CBCarlos BeltránUniversidad de Cantabria FCF. CarrascoUniversidad de la República de Uruguay DFDamir FerizovićKU Leuven

Key Points

The study aims to explore the distribution of rotation matrices on the special orthogonal group SO(3) with a focus on minimizing logarithmic energy.
Constructed r points on the sphere from zeros of a randomly chosen degree r polynomial.
Considered sets of s evenly distributed rotation matrices at each of the r points.
Analyzed the associated logarithmic energy of these randomized collections.
Identified a construction yielding the lowest expected logarithmic energy.
Establishes a new upper bound on minimal logarithmic energy for n=rs rotation matrices.

Abstract

Abstract We describe several randomized collections of 3 3 3 × 3 rotation matrices and analyze their associated logarithmic energy. The best one (that is, the one attaining the lowest expected logarithmic energy) is constructed by choosing r points on the sphere, which come from the zeros of a randomly chosen degree r polynomial, and considering at each of these points a set of s evenly distributed rotation matrices. This construction yields a new upper bound on the minimal logarithmic energy of n=rs n = r s rotation matrices.

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Cite This Study

Beltrán et al. (Thu,) studied this question.

synapsesocial.com/papers/69d0af36659487ece0fa51a4 https://doi.org/https://doi.org/10.1007/s00365-026-09748-5

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