Generalization of Laws of Mechanics of Continua for Multidimensional Case

Generalization of equations of mechanics of continua for the multidimensional (n>3) case is proposed which is based on a special method of introducing the vector product in the multidimensional Euclidean space. Models of multidimensional elastic, isotropic, and rigid bodies are derived. It is shown that for the case of a multidimensional linearly-elastic isotropic body, the number of elastic constants is 2, as in the 3-D case. For the model of multidimensional rigid body, a tensor equation of angular momentum change is deduced; it is shown that this equation written in the component form coincides with Euler-Arnold equations. Using the tensor form, the explicit representations are obtained for first integrals of the equation of angular momentum change.