Remark on integrable deformations of the Euler top

The Euler top describes a free rotation of a rigid body about its center of mass and provides an important example of a completely integrable system. A salient feature of its first integrals is that, up to a reparametrization of time, they uniquely determine the dynamical equations themselves. In this note, this property is used to construct integrable deformations of the Euler top.