TABLE OF CONTENTS The simplified (linear) equations of motion presented in this appendix represent a modal approach to both of these closely allied rotor instabilities. They are intended as an approximate, but reasonably representative and unified, analysis of the two phenomena and should thereby maximize insights into their respective physics. Although the equations are not intended for general analysis applications in support of actual helicopter design efforts, they nevertheless serve three useful functions. They provide 1) a vehicle for identifying the principal coupling terms inherent in these phenomena, 2) cost-effective "first cuts" at the stability characteristics, and 3) a basis for expansion of the equations to other rotor-pylon coupled phenomena in the form of dynamic equation "building blocks." The assumptions leading to the equations of motion are first presented; the equations themselves are then presented with abbreviated mathematical development that derives from the principles put forth in the text.
The principal assumption made in this analytical formulation is that both the ground- and air-resonance phenomena can be adequately modeled using linear constant coefficient differential equations of motion. That ground resonance can be so modeled has been adequately verified experimentally [see Bielawa, 1962], and the use of linear analyses is thus well-established. However, the assumption that air resonance can also be modeled using only linear differential equations is less secure, and certain nonlinearities must be addressed and linearized for inclusion when appropriate. The predominance of linearity is recognized, however, on the basis that air resonance is basically a phenomenon closely akin...
