The determination of the mechanical parameters of the general uniform polygonal lamina

Abstract

The motion of rigid bodies infields of force depends on their mass, mass-centre location and moments of inertia. These fundamental quantities, here referred to as mechanical parameters. are determined for the general uniform polygonal lamina. The precise description of polygons through border vectors is followed by the determination of the mechanical parameters of elemental triangular laminae. Introducing a general function o.f area, m-area, effectively integrates the separate parameters so that the study's central theorem, extending the results of triangular laminae, involves only m-area. As the worked example illustrates, the theorem permits easy evaluation of numerical results and lends itself well for computerization purposes.