So far our text, drawings, and videos have shown the yaw axis reaction to disturbances. In fact, everything that applies to yaw also applies to pitch. For this next example we switch to the pitch axis because it presents an easier to imagine example. But again, this newest example applies equally well to the yaw axis or any other named gimbal axis.
When we suggest that a gimbal axis is immune to the affects of the 3-DOF of angular acceleration, we actually mean to state a very specific case where the rotational center of the angular disturbance is coincident with the axis pivot under analysis. However, this is not the case for most disturbances. Consider a gust of wind impinging on an airframe (shown in brown in the video). The airframe will pivot in reaction to the gust around its own CG (larger CG symbol). When this happens the entire gimbal will move through an arcing motion that approximates a linear translation for our intents and purposes. This approximation acts upon the gimbal axis shown because the axis CG (the mostly hidden smaller symbol) is not coincident with the axis pivot.
You might observe the video and think that by purposely setting the CG low on the example pitch axis will help provide a natural stability against pitching disturbances. In reality this will not work. Although it appears to provide the needed correction, in practice it will be impossible to set it up for all rates of accelerations. Furthermore, the practice of purposely setting the CG low will absolutely harm the stability for relevant translational accelerations. Again, the single best thing that you can do is to correct the axis CG so that it is coincident with its respective pivot.