# Study of Systems of Active Vibration Protection of Navigation Instrument Equipment
###### Abstract  
Assessment of the influence of vibration isolator parameters on the distribution of the system's natural frequencies is a significant task in the design of vibration isolation systems. The root method was used to determine the natural frequencies of the controlled vibration isolator. For a certain feedback structure of a controlled electrodynamic type vibration isolator, the need for a consistent selection of parameters has been justified. A mathematical solution has been proposed for the approximate determination of the roots of the characteristic equation of the controlled vibration isolator, which enables the analytical assessment of the influence of the vibration isolator parameters on the distribution of its natural frequencies. The research has been conducted in relative parameters, which makes it possible to generalize the results. The specificity of the inertial dynamic vibration isolator, which in some cases is associated with the implementation of anti-resonance conditions, can lead to the fact that resonant frequencies can occur on both sides of the tuning frequency of the vibration isolator. The use of an elastic suspension on flat springs to protect navigation equipment from vibration allows reduction in the intensity of translational vibration, while not changing the orientation of the device relative to the Earth. The implementation of an elastic suspension according to the scheme of the inverted pendulum allows an increase in the effectiveness of vibration isolation, under the conditions of a controlled change of the vibration isolator parameters and due to the use of feedback. The results of this research can be used in precision systems, such as vibration isolators, laser processing equipment, ultraprecision measurements or medical devices. vibration isolator; resonance; mathematical model; root method; kinematic disturbances; low-frequency oscillations 2024 202  
vibration for ground-based instrument navigation equipment is a necessary condition for increasing the accuracy of such systems and, as a result, increasing the safety of air and sea vessels. Increasing the accuracy of determining the navigational parameters of the movement of air and sea vessels will lead to fuel savings for aircraft due to the reduction in the deviation of the real trajectory of the vessels from the calculated one, as well as to the reduction in unforeseen expenses of ship owners. Most modern navigation devices use the compensation method of azimuth measurement [1], in which the output signal of the device is the voltage on the windings of the feedback torque sensor (TS). The scheme shown in Figure 1 is used in the tasks of vibration protection of devices, apparatus, and other precise mechanisms, which are sensitive to vibrations and installed on oscillating bases or on moving objects. The vibration isolation device is the most important part of the anti-vibration system and its purpose is to create such a mode of movement, which is initiated by given excitations, that the purpose of protecting the object is realized. In many cases, this is achievable when using a vibration isolation device. Vibration isolators are devices that are used to protect machines and equipment from the effects of vibration and shock loads. A controlled vibration isolator is an integral part of many precision systems, such as laser processing equipment, medical devices, precision sensors, ultraprecision machining and ultraprecise measurements [2; 3; 4; 5; 6]. In order to ensure the maximum accuracy and stability of the operation of such systems, it is necessary to know the natural frequencies of the controlled vibration isolator [7; 8; 9]. The root method can be used to determine the natural frequencies of the controlled vibration isolator. This method is based on finding the roots of the characteristic equation of the system. The characteristic equation is an equation that determines the dynamic behavior of the system under the influence of external factors.