数学建模及其应用

对浙闽地区的一种传统地方民俗文化活动——板凳龙进行分析研究，建立龙头运动的常微分方程模型、龙身和龙尾运动的递推模型和调头曲线模型.板凳龙在行进过程中可能发生碰撞，本文建立了板凳碰撞的判别模型，给出了相应的判别条件，并在各板凳不碰撞的情况下，确定最小螺距和龙头的最大速度.

In this paper, bench loong, a traditional local cultural activity in Zhejiang and Fujian provinces, are studied. The ordinary differential equation model for the movement of the head, a recursive model for the movement of the bodies and tail, and a turning curve model are established. During the procession of the bench loong, collisions may occur. In this paper, discriminant model for bench collisions is presented, and the corresponding criteria are given. Meanwhile, under the situation of non-collision between the benches, the minimum pitch and the maximum speed of the head are determined.