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PentaKon
PentaKon
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Assuming the matrices you have are pure rotation matrices (i.e. they do not contain scale information) and describe a rotation around an axis which is the same as the one you want to calculate the angular velocity for, then you can extract their angle \$θ\$ directly.

A rotation of angle \$θ\$ around axis \$z\$ in 3D space for example is described by the augmented matrix $$R=\begin{pmatrix} \cos\theta & -\sin\theta & 0 & 0\\ \sin\theta & \cos\theta & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{pmatrix}.$$ HopefullyIt is possible that you do not have the augmented matrix at hand in which case it will be a 3x3 matrix with the last row and last column trimmed off.

Hopefully the matrices you have are of a similar form (i.e. they describe a rotation around one of the basis vectors). Once you have extracted \$θ_0\$ and \$θ_1\$ you can find their difference \$Δθ\$ and from there you can use the angular velocity formula $$ ω = \frac{Δθ}{Δt} $$ If the matrices you have are not around one of the basis vectors then this becomes more complicated and I'm not sure how to approach this since you might not even know around which axisbut the rotation happenslogic stands. Check this for rotation matrices around an arbitrary axis

Assuming the matrices you have are pure rotation matrices (i.e. they do not contain scale information) and describe a rotation around an axis which is the same as the one you want to calculate the angular velocity for, then you can extract their angle \$θ\$ directly.

A rotation of angle \$θ\$ around axis \$z\$ in 3D space for example is described by the matrix $$R=\begin{pmatrix} \cos\theta & -\sin\theta & 0 & 0\\ \sin\theta & \cos\theta & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{pmatrix}.$$ Hopefully the matrices you have are of a similar form (i.e. they describe a rotation around one of the basis vectors). Once you have extracted \$θ_0\$ and \$θ_1\$ you can find their difference \$Δθ\$ and from there you can use the angular velocity formula $$ ω = \frac{Δθ}{Δt} $$ If the matrices you have are not around one of the basis vectors then this becomes more complicated and I'm not sure how to approach this since you might not even know around which axis the rotation happens.

Assuming the matrices you have are pure rotation matrices (i.e. they do not contain scale information) and describe a rotation around an axis which is the same as the one you want to calculate the angular velocity for, then you can extract their angle \$θ\$ directly.

A rotation of angle \$θ\$ around axis \$z\$ in 3D space for example is described by the augmented matrix $$R=\begin{pmatrix} \cos\theta & -\sin\theta & 0 & 0\\ \sin\theta & \cos\theta & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{pmatrix}.$$ It is possible that you do not have the augmented matrix at hand in which case it will be a 3x3 matrix with the last row and last column trimmed off.

Hopefully the matrices you have are of a similar form (i.e. they describe a rotation around one of the basis vectors). Once you have extracted \$θ_0\$ and \$θ_1\$ you can find their difference \$Δθ\$ and from there you can use the angular velocity formula $$ ω = \frac{Δθ}{Δt} $$ If the matrices you have are not around one of the basis vectors then this becomes more complicated but the logic stands. Check this for rotation matrices around an arbitrary axis

Source Link
PentaKon
PentaKon
  • 358
  • 1
  • 10

Assuming the matrices you have are pure rotation matrices (i.e. they do not contain scale information) and describe a rotation around an axis which is the same as the one you want to calculate the angular velocity for, then you can extract their angle \$θ\$ directly.

A rotation of angle \$θ\$ around axis \$z\$ in 3D space for example is described by the matrix $$R=\begin{pmatrix} \cos\theta & -\sin\theta & 0 & 0\\ \sin\theta & \cos\theta & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{pmatrix}.$$ Hopefully the matrices you have are of a similar form (i.e. they describe a rotation around one of the basis vectors). Once you have extracted \$θ_0\$ and \$θ_1\$ you can find their difference \$Δθ\$ and from there you can use the angular velocity formula $$ ω = \frac{Δθ}{Δt} $$ If the matrices you have are not around one of the basis vectors then this becomes more complicated and I'm not sure how to approach this since you might not even know around which axis the rotation happens.