This paper describes dynamic formulations for a multi-physics system consisting of an electrical generator and a finite element model of a variable-length cable attached at one end to a reeling mechanism and the other to a rigid body that represents a flying wing. Lie group methods are utilized to obtain singularity-free dynamics of the wing. Two different methods are employed for the derivation and integration of the Euler–Lagrange equations. In the first method, the equations of motion are derived in continuous-time and integrated by a general-purpose implicit ODE solver. The second is the application of the discrete analogue of Lagrange–d’Alembert principle that yields a variational integrator. Extensive simulations are carried out to calculate the computational complexity of the discrete integrator and compare the results for CPU time and accuracy to those of the ODE solver. It is shown that the variational integrator has a significant advantage in terms of preservation of the orthogonality of the wing’s attitude matrix and reduction of the CPU time. The descriptions of the implemented aerodynamic models and controllers, along with the results for the simulation of a tethered-wing system operating in a turbulent wind environment are also presented.

本文描述了一种多物理场系统的动力学公式，该系统由一个发电机和一个可变长度电缆的有限元模型组成，该模型的一端附接到绕线机构上，另一端附接到代表飞翼的刚体上。利用李群方法获得机翼的无奇点动力学。欧拉-拉格朗日方程的推导和积分采用两种不同的方法。在第一种方法中，运动方程是连续时间导出的，并由通用隐式ODE求解器进行积分。第二个是拉格朗日-德阿莱姆伯特原理的离散模拟的应用，它产生了一个变分积分器。进行了广泛的仿真，以计算离散积分器的计算复杂度，并将CPU时间和精度的结果与ODE求解器的结果进行比较。结果表明，在保持机翼姿态矩阵的正交性和减少CPU时间方面，变分积分器具有显着的优势。还介绍了已实现的空气动力学模型和控制器的描述，以及在湍流风环境下运行的系链机翼系统的仿真结果。