Euler's Equations (rigid Body Dynamics)

Euler's Equations (rigid Body Dynamics)

This page discusses rigid body dynamics. For other uses, see Euler function (disambiguation).

In classical mechanics, Euler's equations describe the rotation of a rigid body, using a rotating reference frame with its axes fixed to the body and parallel to the body's principal axes of inertia. In cartesian components, they are:

\begin{align} I_1\dot{\omega}_{1}+(I_3-I_2)\omega_2\omega_3 &= M_{1}\\ I_2\dot{\omega}_{2}+(I_1-I_3)\omega_3\omega_1 &= M_{2}\\ I_3\dot{\omega}_{3}+(I_2-I_1)\omega_1\omega_2 &= M_{3} \end{align}

where Mk are the components of the applied torques M, Ik are the principal moments of inertia I and ωk are the components of the angular velocity ω along the principal axes.

Read more about Euler's Equations (rigid Body Dynamics):  Motivation and Derivation, Torque-free Solutions, Generalizations

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