In this paper, we establish a mathematical model to simulate the dynamic behavior of the high-altitude zero-pressure balloon system during the ground dynamic launching process. The dynamic launching mathematical model includes the solution of the bubble shape and the dynamics model derived by taking the bubble, the membrane bundle, the cable, and the gondola as a whole. The bubble shape is considered as a combination of zero circumferential stress shape at the bottom and fully expanded shape at the top. Under the hypothesis, we use the multiple shooting method and the sequential quadratic programming method together to solve the partially expanded shape in the lower bubble region. Based on bubble shapes, the bubble is modeled as a “spring damping system” and we can establish its dynamic model. The “membrane bundle-cable system” is equivalent to a variable mass rope structure and we solve its dynamic behavior by using the mass particle model. We calculate the swing angle of the gondola by its geometry constraint and force analyses. The Hertz contact model and the Coulomb friction law are used to analyzing the contact between the “membrane bundle-cable system” and the ground or the main boom of the launching vehicle. Based on these dynamic models, we calculate the dynamic launching simulation under three operating conditions of the launching vehicle, which corresponds to three ambient wind speeds. The three operational modes of the launching vehicle are the static operation (2 m/s wind speed), the forward operation to chase the bubble (4 m/s), and the backward operation to increase the gondola releasing angle (0 m/s). We analyze the influence of the wind speed and the launching vehicle action on the force and geometric time history of the dynamic launching system. Furthermore, we discuss the three times typical overload in the dynamic launching system and its influencing factors, which are the opening of the roller, the straightening of the “membrane bundle-cable system” and the releasing of the gondola. The purpose of this paper is to present a set of methods and models for the dynamic launching simulation. It not only calculates the shapes of the bubble and simulates the motion of the quasi rope structure system individually, but also the bubble, the “membrane bundle-cable system” and the gondola are combined to establish a complete set of dynamic models to reflect the main characteristics of the dynamic launching process.

在本文中，我们建立了一个数学模型来模拟高空零压气球系统在地面动态发射过程中的动态行为。动态下水数学模型包括气泡形状的求解和以气泡、膜束、缆索、吊篮为整体推导出的动力学模型。气泡形状被认为是底部零周向应力形状和顶部完全膨胀形状的组合。在该假设下，我们将多次射击方法和顺序二次规划方法结合起来，求解下部气泡区域的部分膨胀形状。根据气泡形状，将气泡建模为“弹簧阻尼系统”，我们可以建立其动力学模型。“膜束-缆索系统”相当于一个变质量绳索结构，我们使用质量粒子模型求解其动力学行为。我们通过几何约束和力分析来计算吊篮的摆动角度。赫兹接触模型和库仑摩擦定律用于分析“膜束-索系统”与地面或运载火箭主臂之间的接触。基于这些动力学模型，我们计算了运载火箭在三种工况下的动态发射仿真，对应于三种环境风速。发射车的三种操作模式为静止操作（2 m/s风速）、向前追泡操作（4 m/s）和向后操作增加吊舱释放角度（0 m/s） ）。我们分析了风速和发射车动作对动态发射系统的力和几何时程的影响。此外，我们讨论了动态发射系统中的三倍典型过载及其影响因素，即滚轮的打开、“膜束-索系统”的矫直和吊篮的释放。本文的目的是提出一套动态发射仿真的方法和模型。它不仅单独计算气泡的形状，模拟拟绳结构系统的运动，而且将气泡、“膜束-索系统”和吊篮结合起来建立一套完整的动力学模型，以反映动态发射过程的主要特征。