# Study of Systems of Active Vibration Protection of Navigation Instrument Equipment
## 2 Materials and Methods  
Vibration isolation systems can be designed in a complex with the protected object as its integral part (for example, suspensions of railway cars and cars, ship diesel installations, etc.). Otherwise, the design of anti-vibration systems has an individual character and is carried out according to the consequences of static and dynamic calculations (the same devices and equipment, depending on the installation locations, are exposed to excitations that are completely different in form or intensity). In a simple model of the anti-vibration system, which allows study of the spatial movement of the source and the object, both of these bodies are considered as absolutely solid. The set of vibration isolators connecting them forms an elastic suspension. The suspension calculation consists of two parts: static, which consists in the calculation of static reactions and static deformations of vibration isolators; and dynamic, which consists in determining the natural frequencies of the elastically suspended supporting body and calculating the characteristic parameters of its movement. A rationally designed suspension must first of all exclude the possibility of resonance oscillations in the system. Therefore, it is necessary that, with a relatively low level of damping, the frequencies of the dominant harmonics of the external disturbance exceed the largest of the natural frequencies of the system. The quality of vibration protection also largely depends on the mutual proximity of the natural frequencies of the system. By designing suspensions based on the principle of \"convergence\" of natural frequencies (ideally until they completely coincide), it is possible not only to increase the degree of tuning from resonances, but also to make the supported body less sensitive (by displacement) to changes in the direction of the static load. An essential characteristic of suspension is the degree of coherence of the system's own oscillations. All other things being equal, suspensions with full frequency resolution are the most preferable, when a disturbance along any of the generalized coordinates causes oscillations only along this generalized coordinate. Low-frequency vibration is one of the reasons for a significant decrease in the accuracy of precision navigation equipment. The use of passive vibration isolation systems to protect against external vibration disturbance, in this and many other cases, does not have a positive effect. Mostly, this happens due to the impossibility of ensuring relatively low natural frequencies of vibration isolation systems. The introduction into these systems of \"fictitious\" parameters [56; 57], inertial mass, restoring force, and resistance force using the control system, allows reduction in the natural frequency of the vibration isolator, and therefore the intensity of the vibrational disturbance acting on the navigation equipment, and, as a result, an increase in its accuracy. The use of a suspension on vertically located flat springs, built according to the scheme of an inverted pendulum, in vibration isolation systems allows, due to the achievement of a small equivalent stiffness, significant reduction in the transmission of vibration in the horizontal plane. A further reduction of the natural frequency of vibration isolation systems, and therefore a reduction of vibration transmission, is possible due to a controlled change of parameters (stiffness, mass, and resistance), but it is also limited by the need for a coordinated selection of gain coefficients value and the dynamics of individual feedback parts, determined by the stability condition. Due to the fact that, when using feedback, the order of equations that describe the dynamics of a vibration isolator increases, the calculation of its characteristics, in particular natural frequencies and the effectiveness of vibration isolation, is carried out by computational methods.