Points on SO (3) with low logarithmic energy

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.