112. Inertial Principal Axes as an Eigenvalue Problem

Paper

Abstract

Inertia calculations in the past have been of a symmetrical nature and hence not really been perplexing to the weight engineer. A simple transformation to move the coordinate axes to the center of gravity of the body (and occasionally a rotation in a single direction) has been the outstanding problem and its solution is found in any engineering handbook. It has meant a direct transformation incorporated in the inertia formulas or the additions of Io term ( or the determination of an angle of rotation.) Recently, however, unsymmetrical conditions have arisen either from externals stores of unequal weight or the location of equipment in and unsymmetrical fashion (which produced rotational angles in two directions, laterally and vertically). The former produces sizable products of inertia and the latter but slight products. We shall see how even slight differences in the inertias can affect the equations of motion especially at high speeds.