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

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 x 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.