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Some years ago, there was that question on this forum:"How to quantify noncommutativity?".

I am asking that question in a context, human movement, which implies kinematic chains (like in robotics, series of rotating joints linked rigidly) including rotations in 3D and 2D, depending on the anatomy of the joint, hence SO(3), and SO(2) respectively. When moving the body it is known that the brain and mechanical constraints often couple rotations and simplify the "control" of motion by reducing the dimension of the manifold (it's called a "synergy" in neuroscience or physiology). There is a possibility, not explored, that this has also an effect on the "degree to which" motion remains SO(3) and is therefore non commutative. I wonder if mathematical tools can help quantifying the extent to which those couplings among rotations reduce the non commutativity of human body motion

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  • $\begingroup$ Just as a side remark: there are also hinge joints, i.e. joints with 1D rotation. $\endgroup$
    – Lukas Lewark
    Commented Feb 10, 2022 at 20:05
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    $\begingroup$ I’m voting to close this question because this seems like a fascinating area for exploration, but it seems way too broad to be appropriate as an MO question. $\endgroup$
    – LSpice
    Commented Feb 10, 2022 at 21:49
  • $\begingroup$ @julien lagarde It appears what you describe here is the context / motivation of / for your problem. What is missing is the actual math question, stripped of all non-math details. For example, "I wonder if mathematical tools can help quantifying the extent to which those couplings among rotations reduce the non commutativity of human body motion" is not a math question, it's a question about modeling human body motion. $\endgroup$
    – dohmatob
    Commented Feb 11, 2022 at 14:24
  • $\begingroup$ What about this: if rotations are going back and forth between 2D and 3D space, is there a way to estimate the frequency of occurence of non commutative motion? $\endgroup$
    – julien lagarde
    Commented Feb 19, 2022 at 18:57
  • $\begingroup$ mathoverflow.net/questions/96690/… $\endgroup$
    – julien lagarde
    Commented Apr 14, 2022 at 8:23

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