A simplified vibration analysis of an airplane considers bounce and pitch motions (Fig. 6.24(a)). For this, a model consisting of a rigid bar (corresponding to the body of the airplane) supported on two springs (corresponding to the stiffnesses of the main and nose landing gears) as shown in Fig. 6.24(b) is used. The analysis can be conducted using three different coordinate systems as shown in Figs. 6.24(c)-(e). Derive the equations of motion in the three coordinate systems and identify the type of coupling associated with each coordinate system.

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k m. Jo G + (a) FIGURE 6.24 Modeling of an airplane. (b) k