Dynamical Systems Theory

Dynamical Systems Theory studies how systems evolve over time based on their current conditions and governing laws. In Lagrangian mechanics, it focuses on energy and motion, while in celestial mechanics, it analyzes the motion of celestial bodies under gravitational forces. By using mathematical models, this theory helps predict complex behaviors, like the orbit of planets or the dynamics of chaotic systems. It emphasizes understanding the relationships between variables and how small changes can lead to significant differences in outcomes, providing insight into both orderly and chaotic processes in nature.