Editing Infinitesimal rotation matrix (section)

==Discussion==
An '''infinitesimal rotation matrix''' is a [[skew-symmetric matrix]] where:
* As any [[rotation matrix]] has a single real eigenvalue, which is equal to +1, the corresponding [[eigenvector]] defines the [[rotation axis]].
* Its module defines an infinitesimal [[angular displacement]].

The shape of the matrix is as follows:
<math display="block">
  A = \begin{pmatrix}
     1          & -d\phi_z(t) &  d\phi_y(t) \\
     d\phi_z(t) &  1          & -d\phi_x(t) \\
    -d\phi_y(t) &  d\phi_x(t) &  1 \\
  \end{pmatrix}
</math>

===Associated quantities===
Associated to an infinitesimal rotation matrix <math>A</math> is an ''[[infinitesimal rotation tensor]]'' <math>d\Phi(t) = A - I</math>:

<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>
\Omega = \frac{d\Phi(t)}{dt} = \begin{pmatrix}
   0           & -\omega_z(t) &  \omega_y(t) \\
   \omega_z(t) &  0           & -\omega_x(t) \\
  -\omega_y(t) &  \omega_x(t) &  0           \\
\end{pmatrix}
</math>