Better explain the TMT calculation for inertia forces#228
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Fixes #217 Shows more carefully how to calculate the inerital forces that are linear in the velocities (Coriolis, gyroscopic, centripital). It is worth noting that Euler's equation is: dH/dt = Iw'' + w x (Iw) and is equivalent to: dH/dt = I'w + Iw' but when grouping linear and rotational equation in one single big matrix equation you can't write the cross product form because it only applies to a 3D vector. You can probably write this succintly with the Clifford Algebra based dynamics approaches. It still seems that papers leave out the I'w term (but that might because they are only about 2D systems). This confused me several times.
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@Peter230655 @phdejong you both may be interested in this. If either of you are willing to review my explanation and math on this one, that is appreciated. |
moorepants
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Apr 17, 2026
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Fixes #217
Shows more carefully how to calculate the inerital forces that are linear in the velocities (Coriolis, gyroscopic, centripital). It is worth noting that Euler's equation is:
dH/dt = Iw' + w x (Iw)
and is equivalent to:
dH/dt = I'w + Iw'
but when grouping linear and rotational equation in one single big matrix equation you can't write the cross product form because it only applies to a 3D vector. You can probably write this succintly with the Clifford Algebra based dynamics approaches.
It still seems that papers leave out the I'w term (but that might because they are only about 2D systems). This confused me several times.