Euler's Equations (rigid Body Dynamics) | Euler 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 M_k are the components of the applied torques M, I_k are the principal moments of inertia I and ω_k 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

Famous quotes containing the word body:

“We know now that the soul is the body, and the body the soul. They tell us they are different because they want to persuade us that we can keep our souls if we let them make slaves of our bodies.”
—George Bernard Shaw (1856–1950)