A review of some basic aspects related to integration of airplane’s equations of motion

• Main Authors: Dan TURCANU, Laurentiu MORARU
• Format: Article
• Language: English
• Published: National Institute for Aerospace Research “Elie Carafoli” - INCAS 2017-09-01
• Series: INCAS Bulletin
• Subjects: Flight Dynamics Simulation; Controls
• Online Access: http://bulletin.incas.ro/files/turcanu__moraru__vol_9_iss_3.pdf

Numerical integration of the airplane’s equations of motion has long been considered among the most fundamental calculations in airplane’s analysis. Numerical algorithms have been implemented and experimentally validated. However, the need for superior speed and accuracy is still very topical, as, nowadays, various optimization algorithms rely heavily on data generated from the integration of the equations of motion and having access to larger amounts of data can increase the quality of the optimization. Now, for a number of decades, engineers have relied heavily on commercial codes based on automatically selected integration steps. However, optimally chosen constant integration steps can save time and allows for larger numbers of integrations to be performed. Yet, the basic papers that presented the fundamentals of numerical integration, as applied to airplane’s equations of motion are nowadays not easy to locate. Consequently, this paper presents a review of basic aspects related to the integration of airplane’s equation of motion. The discussion covers fundamentals of longitudinal and lateral-directional motion as well as the implementation of some numerical integration methods. The relation between numerical integration steps, accuracy, computational resource usage, numerical stability and their relation with the parameters describing the dynamic response of the airplane is considered and suggestions are presented for a faster yet accurate numerical integration.