Euler's Equations of Motion for Rotation of Rigid Body/Also presented as
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Euler's Equations of Motion for Rotation of Rigid Body: Also known as
Euler's Equations of Motion for Rotation of Rigid Body can also be seen presented in the form:
\(\ds I_1 \dfrac {\partial \omega_1} {\partial t} - \paren {I_2 - I_3} \omega_2 \omega_3\) | \(=\) | \(\ds M_1\) | ||||||||||||
\(\ds I_2 \dfrac {\partial \omega_2} {\partial t} - \paren {I_3 - I_1} \omega_3 \omega_1\) | \(=\) | \(\ds M_2\) | ||||||||||||
\(\ds I_3 \dfrac {\partial \omega_3} {\partial t} - \paren {I_1 - I_2} \omega_1 \omega_2\) | \(=\) | \(\ds M_3\) |
where:
- $I_1$, $I_2$ and $I_1$ are the components of the torque applied about the principal axes
- $I_1$, $I_2$ and $I_1$ are the moments of inertia at fixed point $O$
- $\omega_1$, $\omega_2$ and $\omega_3$ are the components of angular velocity along the principal axis.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Euler's equations
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Euler's equations