Equivalent Forms of the System of Equations of the Projectile's Nutritional Vibrations

Abstract

When carrying out scientific research on the modernization of existing artillery weapons and the creation of new ones, the problem of solving the inverse problem of external ballistics regarding the restoration of the aerodynamic coefficients of the projectile with a given accuracy remains unsolved. The basis of inverse problems of external ballistics regarding the restoration of aerodynamic coefficients of a projectile are mathematical models (MM) describing the process of its flight, as well as data of external trajectory measurements, which are carried out on the ballistic track using technical means with a specified accuracy. The nature of providing MM projectile flight varies depending on the required degree of reliability of the reflection of the real physical process of projectile flight, adequate consideration of the forces (moments) acting on the projectile, as well as the level of information about external flight conditions. The most suitable (accurate, relatively simple) for restoring the aerodynamic coefficients of the projectile is the modified material point model (MMMT), as the MM of the projectile flight. MMMT takes into account all aerodynamic forces (force coefficients), the orientation of the projectile is characterized by the angles of its nutational oscillation, and the energy balance is taken into account through the angular velocity of the projectile around its axis of symmetry. An important element of the MMMT equations are the equations that determine the behavior of nutational oscillations of the projectile during its flight. The article presents procedures for reducing the system of equations of nutational oscillations of a projectile to a form convenient for restoring its aerodynamic coefficients, as well as developed equivalent versions of the differential equations of nutational oscillations in scalar form. To expand the possibilities of restoring the aerodynamic coefficients of the projectile, equivalent versions of the differential equations of nutational oscillations of the projectile are presented in rectangular and spherical coordinate systems.