Euler's Equations (Rigid Body Dynamics)

Euler's rotation equations describe how a rigid body spins, expressed as a first-order ordinary differential equation for the body's angular velocity vector, written in a reference frame that rotates along with the body itself. They are named for the mathematician Leonhard Euler, who first derived them. When no outside torque acts on the body, the resulting motion is called an Euler top; when the only torque comes from gravity, certain special cases become exactly solvable, as with the Lagrange top.