用数学方法解析飞行轨迹，快且可解释。

Flight trajectory prediction (FTP) and similar time series tasks typically require capturing smooth latent dynamics hidden within noisy signals. However, existing deep learning models face significant challenges of high computational cost and insufficient interpretability due to their complex black-box nature. This paper introduces FlightKooba, a novel modeling approach designed to extract such underlying dynamics analytically. Our framework uniquely integrates HiPPO theory, Koopman operator theory, and control theory. By leveraging Legendre polynomial bases, it constructs Koopman operators analytically, thereby avoiding large-scale parameter training. The method's core strengths lie in its exceptional computational efficiency and inherent interpretability. Experiments on multiple public datasets validate our design philosophy: for signals exhibiting strong periodicity or clear physical laws (e.g., in aviation, meteorology, and traffic flow), FlightKooba delivers competitive prediction accuracy while reducing trainable parameters by several orders of magnitude and achieving the fastest training speed. Furthermore, we analyze the model's theoretical boundaries, clarifying its inherent low-pass filtering characteristics that render it unsuitable for sequences dominated by high-frequency noise. In summary, FlightKooba offers a powerful, efficient, and interpretable new alternative for time series analysis, particularly in resource-constrained environments.