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m →Matrix analysis: fixed "If we the" to "If the" |
Kishore178 (talk | contribs) Fix sign of the Euler equations (also fixed the sign in the other required places). After this edit, the form of the Euler equations mentioned here will be consistent with that mentioned in the page for Euler's rotation equations (the correct one, IMO) |
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Line 20:
<math display="block">
\begin{align}
I_1\dot{\omega}_1 &= -(I_3-I_2)\omega_3\omega_2~~~~~~~~~~~~~~~~~~~~\text{(1)}\\
I_2\dot{\omega}_2 &= -(I_1-I_3)\omega_1\omega_3~~~~~~~~~~~~~~~~~~~~\text{(2)}\\
I_3\dot{\omega}_3 &= -(I_2-I_1)\omega_2\omega_1~~~~~~~~~~~~~~~~~~~~\text{(3)}
\end{align}
</math>
Line 35:
<math display="block">
\begin{align}
I_2 \ddot{\omega}_2 &= -(I_1-I_3) \omega_1\dot{\omega}_3 \\
I_3 I_2 \ddot{\omega}_2 &= (I_1-I_3) (I_2-I_1)(\omega_1)^2\omega_2 \\
\text{i.e. }~~~~ \ddot{\omega}_2 &= \text{(negative quantity)} \cdot \omega_2
Line 67:
\end{bmatrix} =
\begin{bmatrix}
0 & -\omega_3(I_3-I_2)/I_1 \\
-\omega_3(I_1 - I_3)/I_2 & 0
\end{bmatrix} \begin{bmatrix}
\omega_1\\
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