METHODOLOGICAL FOUNDATIONS FOR APPLYING UAV DYNAMICS PROBLEMS IN HIGHER MATHEMATICS COURSE FOR AVIATION SPECIALTIES

Abstract

DOI: https://doi.org/10.26565/2074-8922-2026-86-21

Purpose. The aim of this article is to substantiate the feasibility and develop a methodological approach to integrating applied problems related to unmanned aerial vehicle (UAV) flight dynamics modeling into the teaching of the "Differential Equations" section within the Higher Mathematics course for students of specialty J6 "Aviation Transport". The relevance of the study is determined by the growing role of UAVs in the modern aviation industry and the need to strengthen the applied orientation of fundamental mathematical training for future aviation professionals.

Methods. The study was conducted at the Department of Information Technologies and Aviation Robotic Systems of the Ukrainian State Flight Academy. The methodological basis comprises the competency-based approach, principles of interdisciplinary integration and STEM education. A comparative analysis of the syllabi for "Higher Mathematics" and "Unmanned Aerial Vehicle Control" within specialty J6 "Aviation Transport" was carried out. Methods of systems analysis, mathematical modeling, and pedagogical design were employed to establish interdisciplinary connections between the mathematical apparatus of differential equations and UAV flight dynamics problems.

Results. Direct correspondences were established between the types of differential equations studied in the Higher Mathematics course and mathematical models of UAV motion. Three mathematical models adapted for the educational process were developed. First-order differential equations with separable variables were shown to describe the rectilinear motion of a UAV with aerodynamic drag, in particular the vertical takeoff of a quadcopter. Second-order linear homogeneous differential equations with constant coefficients were used to model the longitudinal stability of the aircraft based on the roots of the characteristic equation. Non-homogeneous linear equations with a special right-hand side were applied to describe the UAV response to periodic external disturbances such as wind gusts or engine vibrations, including resonance analysis. Analytical solutions were derived for each model and interpreted in terms of real UAV parameters. A set of applied problems with specific numerical parameters was developed for practical sessions and independent study.

Conclusions. The integration of UAV flight dynamics modeling problems into the Higher Mathematics course enhances student motivation, develops general competencies of abstract thinking, analysis and synthesis (GC 09), research capability (GC 04) and information technology skills (GC 03), and ensures the practical orientation of mathematical training for future aviation professionals. The proposed approach is universal for all educational programs within specialty J6 "Aviation Transport" and can be implemented in the educational process of higher aviation education institutions. A promising direction is the development of computer simulations of UAV dynamics to support practical sessions.