Analysis and Modeling Method of Mechanical Behavior Based on Trampoline Movement

Trampoline gymnastics is a high-difficulty sport integrating explosive power, coordination, and precise control. To scientifically guide training protocols and extend equipment service life, this study establishes a multi-phase mathematical model covering the entire trampoline motion process, sequentially addressing athlete takeoff posture optimization, landing impact buffering control, and multi-athlete collaborative jump fatigue analysis.  This study establishes a biomechanical model to analyze the direction, magnitude, and relationship between force application and body posture of a 1.75-meter-tall athlete performing a standardized forward somersault during the takeoff instant. Numerical simulation is employed to validate the model's rationality.  A force exertion posture analysis model based on rigid body dynamics and angular momentum conservation was developed to resolve "how to achieve front flips by adjusting takeoff direction and body posture." By constructing a nonlinear mapping model linking exertion angle, angular velocity, and maneuver completion, the minimum required take off angle (17°–20°) for standard flips was identified. Analysis of posture control strategies for athletes of different body types revealed that medium angles (17°–20°) represent an ideal range balancing maneuver completion and force efficiency.  Dynamic equations are formulated to characterize the forces acting on the athlete from takeoff to landing, determining the landing velocity and impact forces. Without considering the athlete's center of gravity, strategies for minimizing impact forces through adjustments in takeoff height and landing posture are investigated.  A landing impact dynamics model centered on a mass-spring-damper system was constructed to address "how to mitigate landing impacts and enhance safety." By solving nonlinear ODE systems simulating the complete takeoff-flight-landing process, nine landing strategies were evaluated via numerical simulations. The optimal buffering strategy reduced peak impact forces from 4,018 N to 2,847 N, achieving a 29.1% reduction and significantly improving safety performance.  A multi-athlete dynamic model incorporating variables such as body weight and takeoff timing is developed to analyze the stress distribution and fatigue damage of the trampoline under varying conditions. An optimization strategy minimizing fatigue damage is proposed based on weight distribution and synchronized takeoff sequences, with predictions of fatigue life improvement before and after implementation.  A trampoline impact-fatigue evolution coupling model under multi-athlete collaborative conditions was established by integrating fatigue accumulation theory and takeoff sequence optimization. Simulation results indicated that the original sequence achieves local optimization under current settings, but the model can be extended to intensive-use scenarios. Through dynamic scheduling of body weights and take off sequences to avoid force peak superposition, equipment fatigue is markedly delayed.  In summary, this study constructs a comprehensive mechanical analysis framework spanning individual force modeling, motion buffering control, and multi-athlete weight-sequence coordination. It proposes quantifiable, optimizable, and generalizable training strategies and structural lifespan management methods. The developed models exhibit strong universality and interpretability, applicable to competitive training, equipment design, and fatigue assessment scenarios.