基于Lagrange方法的单旋翼飞行器动力学建模

Dynamics modeling for monowing rotorcraft using Lagrange method

为了进行微小型单旋翼飞行器的动力学建模,通过建立多个坐标系来反映各部分间的相对运动。首先,利用坐标变换得到位置、速度及加速度等向量,并代入拉格朗日方程得到运动学模型;然后,对模型进行数值求解,得到飞行器的姿态响应。仿真结果表明,飞行器定点盘旋时合外力为零,能量保持不变;爬升或前飞时有非保守力做正功,能量增大。

For the dynamics modeling for the microminiature monowing rotorcraft,several coordinate systems for different parts of the vehicle were set up to reflect the relative movements. Firstly,vectors such as position,velocity and acceleration were obtained by transformation of coordinates,and substituted into Lagrange equation to get dynamic model. Then,attitude responses were obtained by numerical calculation of the model. Simulation results show that the force is zero and the energy remains constant when the rotorcraft is hovering; non-conservative force works and the energy increase when the rotorcraft is climbing or flying forward.