Hamel coefficients for the rotational motion of an N–dimensional rigid body

Abstract

Many of the kinematic and dynamic concepts relating to rotational motion have been generalized for N–dimensional rigid bodies. In this paper a new derivation of the generalized Euler equations is presented. The development herein of the N–dimensional rotational equations of motion requires the introduction of a new symbol, which is a numerical relative tensor, to relate the elements of an N Ö N skew–symmetric matrix to a vector form. This symbol allows the Hamel coefficients associated with general N–dimensional rotations to be computed. Using these coefficients, Lagrange's equations are written in terms of the angular–velocity components of an N–dimensional rigid body. The new derivation provides a convenient vector form of the equations, allows the study of systems with forcing functions, and allows for the sensitivity of the kinetic energy to the generalized coordinates.