Annotation. Among the various destructive phenomena that negatively affect the harmony of an individual's life, the issue of overcoming the feeling of inferiority takes on special importance. The study of this phenomenon among the population of Ukraine in the modern conditions of martial law and the COVID-19 pandemic is extremely relevant. The aim of the study is to translate, adapt and validate the questionnaire "Comparative Feeling of Inferiority Index", as well as to determine the feeling of inferiority index among student youth with its help. The following descriptive and analytical statistics methods were used in the research: arithmetic mean with standard square deviation (М±SD), percentages with error (Р±m, %), Cronbach's alpha coefficient (α-coefficient), correlation according to Spearman's rank (R). Within the framework of the research, a verified translation of the questionnaire into Ukrainian was carried out for the first time with adaptation of the terminology to the specifics of the language. Pilot testing of the translated questionnaire and repeated re-testing with the same participants was conducted, which proved excellent reliability and diagnostic discriminative ability of the method (R=0.74, p<0.001). The questionnaire was tested on a representative sample (n=612) involving students of higher education institutions of Lviv. The conducted testing proved the validity and high level of reliability of the translated questionnaire: reliable values of internal consistency estimates were obtained according to Cronbach's alpha coefficient – 0.85 for the assessment of a family member and 0.80 for the self-assessment scale. Also, according to the results of the testing, it was established that 7.03±1.03% of the interviewed students had a feeling of Inferiority, and 11.11±1.27% – a feeling of superiority.

When calculating projectile flight trajectories, an urgent issue is the definition and representation of aerodynamic forces (moments) and parameters of the atmosphere, which are significantly non-linear in nature, in the system of mathematical models - differential equations of spatial motion of projectiles. A significant component of the error in determining the aerodynamic force is introduced by the operation of numerical differentiation of tabular values of aerodynamic coefficients, which are included as components in systems of differential equations. In this direction, a scientific approach based on the approximation of the data of aerodynamic coefficients and parameters of the atmosphere by analytical functions is promising, the requirement for which is the possibility of obtaining a single and continuous function within the entire range of changes in the flight parameters of the projectile and ensuring their best approximation to tabular data. A unified approach to the possibility of approximating qualitatively different aerodynamic coefficients and parameters of the atmosphere found further development; as approximating functions, it is proposed to use an analytical function as the sum of a reference function (error function) and a set of basic functions (Gaussian functions), which allows to obtain a continuous-differentiated approximating function on the segment of the change of the projectile flight parameter, which can be represented by a single analytical expression. The obtained values of the single continuous-differentiated on the segment of the change of the projectile flight parameter approximating the function of the aerodynamic coefficients and the parameters of the atmosphere, which are given by a single analytical expression, can be used to solve the problems of calculating Firing tables and preparing data using ballistic integrating algorithms for firing artillery systems. Keywords: aerodynamic forces (moments), parameters of the atmosphere, projectile, approximation, differentiation, analytical expression, error function, Gaussian function.