5D-Euler Equations for Rotating Bodies

The manuscript undertakes a study of the rotational behaviour of rigid bodies in spaces of higher dimensions. The primary objective of the manuscript is the derivation of the 5D Euler equations. The closed-form solutions of the 5D-Euler equations are presented. The visualization of the observable motions and its dependence upon the hypothetical parameters of the 5D-state are demonstrated in closed form. Within the paradigm of four-dimensional Euclidean spaces, the number of rotational degrees of freedom is six. In the case of a five-dimensional Euclidean space, the number of rotational degrees of freedom is increased to ten. The Euler equations are derived using the tensor representation of rotational velocities. The closed-form solutions were discovered for a specific relationship between the principal moments of inertia.