Infinitesimal rotation matrix: Difference between revisions

Revision as of 06:16, 6 September 2023

Revision as of 06:48, 6 September 2023

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===Associated quantities===

Associated to an infinitesimal rotation matrix <math>A</math> is an ''[[infinitesimal rotation tensor]]'' <math>d\Phi(t) = A - I.</math> Dividing it by the time difference yields the ''[[angular velocity tensor]]'':

<math display="block">

d\Phi(t) = \begin{pmatrix}

0 & -d\phi_z(t) & d\phi_y(t) \\

d\phi_z(t) & 0 & -d\phi_x(t) \\

-d\phi_y(t) & d\phi_x(t) & 0 \\

\end{pmatrix}

</math>

Dividing it by the time difference yields the ''[[angular velocity tensor]]'':

:<math>