Research On Speed Strategy of Freestyle Swimming Based on Lagrange Multiplier Method

This study investigates the optimal speed strategies for freestyle swimming events, focusing on balancing speed endurance and tactical approaches across different distances. Using the Lagrange multiplier method and Newton’s iterative method, we developed a speed-distribution model to minimize total swimming time, considering constraints on speed, acceleration, and physical capacity. Additionally, a dynamic model based on game theory was established to describe athletes’ dynamic speed distribution and strategic interactions, incorporating the Hamilton-Pontryagin principle and Nash equilibrium. Results show that short-distance events prioritize explosive power, while middle and long-distance events require balancing energy distribution and managing lactic acid accumulation. This research innovatively integrates mathematical modeling with sports physiology and game theory, providing a comprehensive framework to optimize freestyle swimming strategies and offering scientific recommendations for athletes to enhance performance.