Euler's equations (rigid body dynamics)

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Classical mechanics
${\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}$ Second law of motion
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In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler.

In the absence of applied torques, one obtains the Euler top. When the torques are due to gravity, there are special cases when the motion of the top is integrable.