Tensor Formalism for Rotating Bodies in Multidimensional Euclidian Space

The concepts of torque, angular momentum, and moment of inertia are fundamental to the description of rotational motions. These concepts can be regarded as analogs to the fundamental concepts of force, linear momentum, and mass, which are pivotal to linear motions. The mutual dependence of these physical quantities is predicated on the funda-mental law of dynamics, a foundational principle that governs rotational motion. The rigid body can be used as a model for a piece of ordinary, solid matter; the internal degrees of freedom (such as vibrations) are neglected. This approach offers a distinct pedagogical advantage, whereby many observations concerning the rigid body appear to stem from statements about systems of mass points. The primary objective of the manuscript is the derivation of the 4D Euler equations. The closed-form solutions of the 4D-Euler equations are presented. The visualization of the observable 3D-motions and its dependence upon the hypothetical parameters of the 4D-state are demonstrated in closed form.