Rotating multidimensional rigid bodies

Abstract The primary objective of the present manuscript is the derivation of the Euler equations in multidimensional Euclidean spaces. The method of derivation is based on the common tensor formalism. The kinematic characterization of a rigid body can be defined as a model for an object that is characterized by only one point and an additional orientation in space. An approach involves conceptualizing the multidimensional rigid body as a deformable system comprising a certain number of mass points and subsequently progressing to continuous mass distributions. It is important to note that this transition to continuous mass distributions necessitates additional assumptions. The closed-form solutions of the 4D-Euler equations are presented. The introduction of spin matrices is imperative for the articulation of hypothetical spin mechanics in four-dimensional Euclidean space. The execution of all the spin matrices was conducted in strict accordance with the Euler equations, within the context of four-dimensional Euclidean space. Graphical abstract