simplifies calculations. As described in the moment of inertia article, the angular momentum L can then be written Also in some frames not tied to the body can it be possible to obtain such simple (diagonal tensor) equations for the rate of change of the angular momentum. Then ω must be the angular velocity for rotation of that frames axes instead of the rotation of the body. It is however still required that the chosen axes are still principal axes of inertia. The resulting form of the Euler rotation equations is useful for rotation-symmetric objects that allow some of the principal axes of rotation to be chosen freely. Special case solutions Torque-free precessions Torque-free precessions are non-trivial solution for the situation where the torque on the right hand side is zero. When I is not constant in the external reference frame (i.e. the body is moving and its inertia tensor is not constantly diagonal) then I cannot be pulled through the derivative operator acting on L. In this case I(t) and ω(t) do change together in such a way that the derivative of their product is still zero. This motion can be visualized by Poinsot's construction. See also Euler angles Dzhanibekov effect Moment of inertia Poinsot's construction Rigid rotor References C. A. Truesdell, III (1991) A First Course in Rational Continuum Mechanics. Vol. 1: General Concepts, 2nd ed., Academic Press. . Sects. I.8-10. C. A. Truesdell, III and R. A. Toupin (1960) The Classical Field Theories, in S. Flügge (ed.) Encyclopedia of Physics. Vol. III/1: Principles of Classical Mechanics and Field Theory, Springer-Verlag. Sects. 166–168, 196–197, and 294. Landau L.D. and Lifshitz E.M. (1976) Mechanics, 3rd. ed., Pergamon Press. (hardcover) and (softcover). Goldstein H. (1980) Classical Mechanics, 2nd ed., Addison-Wesley. Symon KR. (1971) Mechanics, 3rd. ed., Addison-Wesley. Rigid bodies Rigid bodies mechanics Rotation in three dimensions Equations de:Eulersche Gleichungen it:Equazioni di Eulero (dinamica)