# Reaction Forces and Apparent Thrust in Dual Oscillating Control Moment Gyroscopes
## 4 Discussion  
First, when the cart was stationary, the front and rear static reaction forces were distributed in proportion to the respective lever arm lengths between the supports and the center of gravity. Second, when a pair of contra-rotating masses was activated, the resulting first component of the inertial force--resembling that of a Dean drive--was also distributed between the front and rear supports according to the same lever arm-based proportionality as the static case. Third, when these contra-rotating masses additionally underwent gyroscopic motion, a second component of the inertial force was generated. This force component was symmetrically shared between the front and rear supports such that any reduction in force at one support corresponded to an equal increase at the other. Using two alternative models--one approximate and the other fully compliant with the initial conditions--this study demonstrated that the generation of internal gyroscopic torque leads to equal-magnitude variations in the support forces (i.e., a couple of equal and opposite forces). It was found that the apparent \"weight loss\" highly depends on the interval of the axles' oscillation. Specifically, when \(-45^{\circ}\leq\theta\leq 45^{\circ}\), the front support, which had the longer lever arm, experienced a local reduction in load, while the rear support correspondingly bore an increased load locally. In contrast, when \(0^{\circ}\leq\theta\leq 45^{\circ}\), the situation was reversed. Having established the behavior of the maximum force values, it is important to emphasize that, over a full cycle, the time integral of the force at each support _vanished_. Consequently, since the net impulse was zero, _no net thrust was generated_ by this device. Regarding the previously reported net thrust (see Figure 1), it should also be noted that in any experimental realization of the reported set-up--or a similar configuration--the static (deadweight) component at each support must be carefully subtracted. For example, if the subtracted value at the front support is even slightly underestimated, then the measured force will not only appear to be reduced, but its time integral will deviate from zero. This may _falsely indicate the presence of a net thrust_. It should be emphasized that there was no intention to undermine the value of prior scientific and technical contributions, as the objective was pursued in good faith. Comparable efforts in the area of inertial propulsion have been undertaken in various countries, as discussed in the following paragraphs. In a previous study regarding inertial propulsion [18], it was reported that efforts to extend the distance traveled through mechanical means date back to ancient times, notably during the Olympic Games. More structured attempts began in Europe during the 1930s and later continued in the United States in the early 1950s [18]. The so-called _Dean drive_ refers to a system composed of two contra-rotating masses that generate an oscillatory unidirectional force which is proportional to the square of the angular velocity (\(\omega^{2}\)) [13,14]. Although it has been claimed that such devices are capable of producing thrust and thereby propelling a vehicle, detailed analyses--including those in [18]--demonstrated that any observed movement is attributable solely to the _initial velocity_ of the rotating masses, rather than sustained propulsion. In simple terms, the operation of the contra-rotating masses mimic a spring-mass system on the ground. Considering the friction between the ground surface and an inertial device, motion is possible [18], as was also demonstrated in [25]. However, the major problem is that even if an initial motion of the cart in the vertical direction becomes possible, when the cart reaches its upper point, there is no more support to produce a second cycle, and so on [19]. Gyroscopes, on the other hand, continue to attract interest among proponents of inertial propulsion.