Anti-gravity technology by non-positive equivalent mass revealing UFO flying secrets

For a long time Unidentified Flying Objects (UFOs) have been reported all the time. On June 25 2021, the US government announced the long-awaited survey report on UFO issues, but did not provide specific answers and called for more research [1]. Investigators conducted investigations into 144 cases of witnessing airplanes or other flying objects flying at mysterious speeds or trajectories, and found no connection with extraterrestrial life, but still came to some conclusions, highlighting the urgency of strengthening the collection of data on US national security issues. The report stated that witnesses to 18 incidents claimed to have found "abnormal" movement patterns or flight characteristics against physics, such as hovering in the air, moving instantaneously, or stopping suddenly during high-speed operation. According to the report, more analysis is needed to determine whether these findings are related to "breakthrough" technologies.

In this paper, a novel kind of anti-gravity technology by non-positive equivalent mass of aircraft is presented also to try to reveal UFO flying secrets [2,3].

Figure 1 shows a two-degree-of-freedom structure [4], where M is the external matrix quality with the displacement U, m is the mass of the internal vibrator with the displacement u, K the spring stiffness between the matrix and vibrator, and $F\sin \omega t$ is the external force with the frequency ${\omega}$.

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According to Newton's second law, there is

$$\begin{equation} \left\{\begin{array}{l} m(\mathrm{d}^{2}u/\mathrm{d}t^{2})+2K(u-U)=0,\\ M(\mathrm{d}^{2}U/\mathrm{d}t^{2})+2K(U-u)=F\sin \omega t. \end{array}\right. \end{equation} \tag{ 1 }$$

Supposing that the movements of U and u are both harmonic with the excited frequency ${\omega}$ and by eliminating u from eq. (1), we can get

$$\begin{equation} F=-\omega^{2}\left(M+\frac{2Km}{2K-m\omega^{2}}\right). \end{equation} \tag{ 2 }$$

If the internal structure of the model is not considered, it can be regarded as an overall structure with equivalent quality [5,6], i.e.,

$$\begin{equation} M_{eff}=M+\frac{2Km}{2K-m\omega^{2}}, \end{equation} \tag{ 3 }$$

which is the dynamic equivalent quality of the two-degree-of-freedom structure plotted with the frequency ${\omega}$ in fig. 2.

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It can be seen from fig. 2 that, with the change of the external excitation frequency$~ \omega$, the dynamic equivalent mass M_eff gradually changes and shows different vibration characteristics [7,8]. When ω is very low, the base and the vibrator keep moving in sync with $M_{eff}=M+m$. As the excitation frequency gradually increases to approach the natural frequency of the vibrator, i.e., $\omega \rightarrow \omega_{1}=\sqrt{2K/m}$, there is $M_{eff}\rightarrow \infty$. At this time, the response of the system is manifested as the local resonance of the vibrator, and the matrix does not respond to external excitation. When $\omega$ is increased to $\omega_{2}=\sqrt{2K(M+m)/(mM)}$, $M_{eff}=0$, in which the structure itself will inevitably produce a great acceleration when it is under force. As the frequency further increases until it approaches infinity, the internal local resonant unit cannot keep up with the vibration of the external matrix and gradually becomes stationary. At this time, $M_{eff}=M$ and the system appears as the vibration of the matrix, as if the internal vibrator is isolated.

In addition, when $\omega_{1}<\omega <\omega_{2}$, we have M_eff  < 0, and this negative equivalent mass means that the structure will move in the opposite direction of the external action force [9].

Therefore, for the two-degree-of-freedom structure shown in fig. 1, it could produce an infinite acceleration under the condition of zero equivalent mass, and provide an opposite movement under gravity with the negative equivalent mass [10]. These two cases with non-positive equivalent mass could both be regarded as a novel kind of anti-gravity technology, which might also explain the UFO flying secrets [11].

Actually any aircraft can be regarded as a multi-degree-of-freedom system driven by engine or other external forces [12,13], also with the inevitable gravity. Once the main excitation peak frequencies of the external actions are known beforehand, the masses of all parts including engines can be carefully designed to obtain the overall zero equivalent mass [14].

For any aircraft, its total mechanical energy is equal to the sum of kinetic energy and potential energy without considering damping, i.e.,

$$\begin{equation} W=T(M,\omega)+U(K,k), \end{equation} \tag{ 4 }$$

where T and U are the kinetic energy and the potential energy of the entire structure when it vibrates, respectively. What needs to be pointed out here is that the kinetic energy is only related to the quality of the structure, and the potential energy is only related to the stiffness of the structure. In general, the total mechanical energy W can be calculated out by using finite element software when the external excitation is known.

Meanwhile, the maximum kinetic energy, the maximum potential energy, and the total mechanical energy are equal to each other as follows:

$$\begin{eqnarray} W&= T_{max}(M,\omega), \end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray} W&= U_{max}(K,k), \end{eqnarray} \tag{ 6 }$$

from which the dynamic equivalent mass and dynamic equivalent stiffness of the structure can be obtained respectively as

$$\begin{eqnarray} M(\omega)&= T_{max}^{-1}(M,\omega), \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} K(\omega)&= U_{max}^{-1}(K,k). \end{eqnarray} \tag{ 8 }$$

According to eq. (7), the whole structure with zero equivalent mass at some frequencies and non-positive frequency range can be figured out once the external input including gravity and engine exciting forces is known. With the designed zero equivalent mass in different directions, the system could produce an infinite acceleration under the corresponding direction, and with the negative equivalent mass it could provide an opposite movement [15]. Thus the anti-gravity technology for any aircraft could be realized in this way.

In order to verify the anti-gravity technology of a multi-degree-of-freedom system excited by an external force, we design a dynamic demonstration experiment of two-degree-of-freedom structure with zero equivalent mass as shown in fig. 3. This structure consists of a matrix mass M and a vibrator mass m connected by a spring K [6], and a softer spring k installed at the bottom. First due to its own gravity there is a static equilibrium position down from the initial position. Then according to eq. (3) we can get the exciting frequency ω for zero equivalent mass once M, m and K are all determined. Under the external excitation force with the frequency ${\omega}$, if this structure could be restored to its initial position, then it must own a corresponding zero equivalent mass to this exciting frequency.

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Figure 4 shows the dynamic process of this structure with zero equivalent mass through the COMSOL simulation analysis. Here $M = 2\ \text{kg}$, $m = 2\ \text{kg}$, $K = 10000\ \text{N/m}$, $k = 2000\ \text{N/m}$. We also analyzed the dynamic characteristics of the system as a function of frequency. When the frequency of the external excitation continues to change, it can be found that the matrix starts to move upward from the static position. It is shown that this structure is restored to its initial position under the external excitation force with the frequency $\omega =\sqrt{2K(m+M)/(mM)}$, which verifies that this system has the zero dynamic equivalent mass corresponding to this frequency.

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With the change of excitation frequency, the reaction force of the matrix and its own equivalent mass both change with the frequency of the external excitation. We can see the trend of this change in fig. 5, the whole change process is divided into three regions: A, B, and C, referring to the three states of equivalent mass, respectively. We can capture the equivalent zero mass point between the B and C, the intersection of the counter-force curve and the equivalent mass curve. We can find that the equivalent quality is close to zero in the area around 22 Hz. From fig. 5, we can see that the frequency range of the equivalent mass change in the near-zero region is relatively narrow. By adjusting the proportional relationship between M and m, the frequency range of the near-zero mass characteristic can be broadened. Another way to adjust the frequency range is to adjust the damping.

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The above analysis is for the undamped system. But in reality, all systems will have damping. Damping will affect the amplitude of the vibration system, in addition to the natural frequency of the system. For an equivalent mass system, the influence of damping is mainly reflected in frequency. Under the influence of damping, damped natural frequency $\omega_{d}=\omega_{1}\sqrt{1-\zeta^{2}}$, ζ is the dimensionless relative damping coefficient, and $0<\zeta <1$. As ζ increases, the gap between $\omega_{d}$ and $\omega_{1}$ will increase, which in turn broadens the frequency range between $\omega_{1}$ and $\omega_{2}$, bringing new ideas to the adjustment of the frequency of the realization of the equivalent mass.

In conclusion, a novel kind of anti-gravity technology by non-positive equivalent mass of aircraft is presented to reveal UFO flying secrets. Through the designed dynamic simulation experiment, zero dynamic equivalent mass of a two-degree-of-freedom system is verified. In this way the non-positive equivalent mass of any aircraft could be figured out once the external input including gravity and engine exciting forces is known, and the anti-gravity technology for any aircraft could be realized.

Data availability statement: All data that support the findings of this study are included within the article (and any supplementary files).