Dynamic analysis of rocket motion using complex functions

Rocket motion is concerned with the study of variable mass systems in which the mass of the system is continuously decreasing. Rockets are propelled forward by the reaction force resulting from the velocity of the exhaust gases. For the accurate analysis of rocket motion and dynamics, differential equations related to changes in mass and force play a very important role. The use of complex power series can be an effective approach in approximating nonlinear functions and analyzing rocket behavior under different conditions. The use of complex numbers allows us to better model complex oscillations and behaviors and to analyze frequencies and dynamic responses. These techniques not only help to better understand the rocket's flight behavior but also provide a strong basis for predicting its motion under changing conditions. In this article, we investigate the effect of complex power series on rocket dynamics and behaviors related to mass changes and show that these concepts can greatly help optimize rocket performance at different stages of flight.