基于Hamilton体系的Lagrange方程盒式倾转旋翼无人机建模

针对倾转旋翼飞行器动态倾转过程中动力学建模问题进行了研究。首先，从多体动力学出发，以某盒式倾转旋翼无人机为算例，将该无人机假设成由机翼、机体、涵道风扇、倾转旋翼等组成的多刚体系统。其次，通过不同刚体质心间的位移约束，建立该无人机系统的非保守力和力矩矩阵，以及动能、势能、余虚功和逆势能模型。最后，分别基于Hamilton体系下的Lagrange方程和第二类Lagrange方程推导并建立了该盒式倾转旋翼无人机的动力学模型。仿真结果表明:两类Lagrange方程所建动力学模型的仿真结果与实验数据一致，验证了所提建模方法的合理性；在倾转旋翼转速不变的情况下，倾转过程所用时间越长，无人机掉高越少，轨迹越光滑，但输入能量越多，具体倾转过程的设计要根据实际输入能量、倾转时间等需求进行确定。 

Modeling of box-wing tilt-rotor UAV based on Lagrange equation in Hamilton system

The dynamics modeling of the tilt-rotor aircraft is studied during dynamic transition process. Firstly, starting from the multibody dynamics, a box-wing tilt-rotor UAV is taken as an example, which is assumed as a multi-rigid-body system consisting of wings, a body, ducted fans, tilt rotors, etc. Secondly, the non-conservative force and moment matrix of the UAV system are established by the displacement constraints of different rigid body centroids, and the kinetic energy, potential energy, complementary virtual work and inverse potential energy of the UAV are established. Finally, based on the Lagrange equation in Hamilton system and the second Lagrange equation, the dynamics model of the box-wing tilt-rotor UAV is deduced and established. The simulation results show that the simulation results of the dynamics models established by the two types of Lagrange equations are consistent with the experimental data, which verifies the rationality of the proposed modeling method. In the case that the rotation speed of the tilt rotor is constant, the longer the transition process takes, the less the UAV is dropped, the smoother the trajectory is, but the more input energy is, and the design of the specific transition process should be determined according to the actual needs of the time that the transition process takes, input energy, etc.