Generalization of Rotational Mechanics and Application to Aerospace Systems

Generalization of Rotational Mechanics and Application to Aerospace Systems. (May 2005) Andrew James Sinclair, B.S., University of Florida; M.S., University of Florida Co–Chairs of Advisory Committee: Dr. John L. Junkins Dr. John E. Hurtado This dissertation addresses the generalization of rigid-body attitude kinematics, dynamics, and control to higher dimensions. A new result is developed that demonstrates the kinematic relationship between the angular velocity in N -dimensions and the derivative of the principal-rotation parameters. A new minimum-parameter description of N -dimensional orientation is directly related to the principal-rotation parameters. The mapping of arbitrary dynamical systems into N -dimensional rotations and the merits of new quasi velocities associated with the rotational motion are studied. A Lagrangian viewpoint is used to investigate the rotational dynamics of N -dimensional rigid bodies through Poincaré’s equations. The N -dimensional, orthogonal angularvelocity components are considered as quasi velocities, creating the Hamel coefficients. Introducing a new numerical relative tensor provides a new expression for these coefficients. This allows the development of a new vector form of the generalized Euler rotational equations. An N -dimensional rigid body is defined as a system whose configuration can be completely described by an N×N proper orthogonal matrix. This matrix can be related to an N×N skew-symmetric orientation matrix. These Cayley orientation variables and the angular-velocity matrix in N -dimensions provide a new connection