- #1

observer1

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I envision the three fundamental rotation matrices: R (where I use R for Ryz, Rzx, Rxy)

I note that if I take (dR/dt * R-transpose) I get a skew-symmetric angular velocity matrix.

(I understand how I obtain this equation... that is not the issue.)

Now I am making the leap to learning about Lie Algebras and Lie Groups

And I understand that any Rotation matrix can be represented with the exponential map

And with the exponential map, the generator of the map happens to have a form that is skew symmetric and (aside from the coefficients) of the same form as the angular velocity matrix.

Of course. A rotatoin matrix is a change. The skew symmetric angular velocity matrix is a RATE of change.

How is it possible for these to related to each other through an exponential map that does not involve TIME.

I note that if I take (dR/dt * R-transpose) I get a skew-symmetric angular velocity matrix.

(I understand how I obtain this equation... that is not the issue.)

Now I am making the leap to learning about Lie Algebras and Lie Groups

And I understand that any Rotation matrix can be represented with the exponential map

And with the exponential map, the generator of the map happens to have a form that is skew symmetric and (aside from the coefficients) of the same form as the angular velocity matrix.

Of course. A rotatoin matrix is a change. The skew symmetric angular velocity matrix is a RATE of change.

How is it possible for these to related to each other through an exponential map that does not involve TIME.

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