AI 中文总结
本文针对泰山跳跃问题的简化模型——从单摆释放的抛体系统，通过解析方法研究其使水平射程最大的最佳释放角，推导了该角的三次方程表征、与初速度的关系及高低初速度极限下的渐近表达式。
AI 中文摘要
本文分析从单摆释放的抛体运动，重点研究使水平射程最大化的最佳释放角及对应的最大射程，该系统是泰山跳跃问题的简化模型。采用简单解析方法，最佳释放角由三次方程表征，且随初速度增大而增大；此外，还推导了低初速度和高初速度极限下最佳角与最大射程的渐近表达式。
英文摘要
The motion of a projectile released from a simple pendulum is analyzed, with particular emphasis on investigating the optimal release angle that maximizes the horizontal range and the corresponding maximum range. This system serves as a simplified model of the Tarzan jump problem. Using simple analytical methods, the optimal release angle is shown to be characterized by a cubic equation and to increase with the initial velocity. In addition, asymptotic expressions for both the optimal angle and maximum range are derived in the limits of low and high initial velocity.
Comments10 pages, 5 figures
