直升机非线性运动方程及其数值分析

基于牛顿法建立了单旋翼带尾桨直升机的非线性运动方程，提出了一种求解直升机非线性运动方程的数值方法。建立方程时，用欧拉角描述直升机在空中的姿态，旋翼采用有挥舞铰且在铰上带有弹性约束的模型，桨盘处的入流采用线性模型，通过对一算例直升机的操纵响应进行数值仿真，将非线性与小扰动线性化的直升机运动方程进行了对比分析。结果表明：从操纵输入到随后的2s左右，非线性和小扰动线性化的直升机运动方程的计算结果非常接近，但在此之后，非线性运动方程的计算结果更能反映直升机的运动规律。

Development of comprehensive nonlinear motion equations for helicopter flight dynamics and numerical simulation

A comprehensive nonlinear flight dynamic model is developed based on Newton approach for a single rotor helicopter in this paper. In the model, Euler angles are used to describe the helicopter attitude, and an elastic hinge rotor is considered, with flap hinge offset and precone angle. A linear inflow model is assumed over the rotor disk. An example for the numerical simulation of helicopter flight dynamics is given and a comparison between the nonlinear model and existing linear model are made. It shows that the two models give the nearly same results until approximately 2 seconds after control inputs have been applied, but after that, the nonlinear model exhibits more realistic motion trends which are characteristic of helicopters.