DIFFERENTIAL EQUATIONS OF THE DEVICE SHELL WITH ARBITRARY GEOMETRY OF THE MERIDIAN LINE

Abstract

The theory describes the shell part of the apparatus as a surface with an arbitrary geometric outline and general acting factors. A mathematical model is constructed, and boundary conditions are formulated to determine the coordinate deformation functions of the shell part under any external disturbances. The methodology for calculating the elastic deformations of its surface with an arbitrary outline of the meridian line is also described. When analyzing the nature of a phenomenon and determining how to combat negative impacts on inertial navigation devices caused by certain factors, it is crucial to calculate the coordinate functions of the deformation of the vehicle's shell under the influence of spatial disturbances. It has been proved that inaccuracies or excessive simplifications lead to errors in the integration of the shell equations, and thus to errors in the calculation of the coordinate functions of the surface deformation and distortion of the meaning of the phenomenon. The equations for determining partial frequencies have been developed, revealing that oscillatory processes on the float's surface affect each other in all directions. Therefore, it is possible to determine the degree of influence for specific mass and dimensional modifications of the RMS. The scientific foundations have been laid for a deep analysis of the dynamics of the vehicle's shell under full-scale conditions. Additionally, a reasoned comparative analysis with the classical cylindrical modification of the float has been revealed. It is now possible to optimize the weight and size characteristics of the device. Theoretical foundations for improving the accuracy and reliability of float devices (and inertial navigation systems in general) are being developed based on passive methods of sound insulation and their combination with other methods, such as active and auto-compensation.