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Context: how to build a VR controller such that swinging it is indistinguishable from swinging a sword.

Is it enough that the controller matches the sword in mass and moment of inertia about the center of mass, to guarantee that swinging one feels like swinging the other?

Do I need higher-order moments of the mass distribution, and how likely are they to produce perceptible differences?

Note that we can assume that the controller is always going to be held in the same way (we don't need to match moment of inertia of a virtual sword being held by the blade, for example).

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To accurately account for how the object feels when rotated through more than one axis (e.g., a turn of the wrist will feel different than swinging with the arm), you will also need the full inertia tensor. This can be fully specified by three numbers, the moments of inertia about the principal axes, instead of just one number for the moment of inertia you were considering in your question.

You will also need to specify the vector displacement of the center of mass of the virtual sword with respect to the location the controller is gripped, and the orientation of the principal axes, so that you can determine the amount of rotation about each axis through the center of mass for any given motion trajectory

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  • $\begingroup$ The idea is to simulate the sword using two "point masses", or heavy spheres, that can slide along a rail coaxial to the controller. The sword is assumed rotationally symmetrical (think a fencing sword), and I might be willing to sacrifice the accuracy of the moment of inertia along the two axes. $\endgroup$
    – Riccardo Orlando
    Commented Feb 3, 2021 at 20:37

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