文章摘要
吴翰1,王正平1,周洲1,2王睿1.拉格朗日方程的菱形翼布局无人机建模[J].空军工程大学学报:自然科学版,2019,20(5):8-15
拉格朗日方程的菱形翼布局无人机建模
A Modeling of Diamond Jointed Wing Configuration UAV Based on Lagrange’s Equation
  
DOI:
中文关键词: 菱形翼布局无人机  拉格朗日方程  凯恩方程  拉格朗日乘子  四元数
英文关键词: diamond joined wing configuration UAV  Lagrange’s equation  Kane equation  Lagrange multipliers  quaternion
基金项目:陕西省重点研发项目
作者单位
吴翰1,王正平1,周洲1,2王睿1 1. 西北工业大学航空学院西安710072 
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中文摘要:
      为建立菱形翼布局无人机的动力学模型,提出一种基于拉格朗日方程的动力学建模方法,首先选取四元数用于参数化该无人机的姿态,建立该无人机系统的约束矩阵;其次通过虚功的形式建立无人机的广义力矩阵,建立无人机的动能与势能模型;最后通过矩阵直积的概念得到与无人机系统约束矩阵乘积为零的矩阵,通过该矩阵消掉拉格朗日方程中的拉格朗日乘子,基于拉格朗日方程模块化地建立该无人机的动力学模型。为与拉格朗日方程进行对比,同样采用Kane方程和ADAMS软件建立该无人机的动力学模型。仿真结果表明,拉格朗日方程、Kane方程以及ADAMS软件的仿真结果基本一致,验证了动力学建模方法的合理性。
英文摘要:
      n order to establish a dynamics model of the diamond jointed wing configuration UAV, a dynamics modeling method based on Lagrange’s equation is proposed. Firstly, the quaternion is selected to parameterize the attitude of the UAV, and the constraint matrix of the UAV system is established. Secondly, a generalized force matrix of the UAV is established by the virtual work, the Kinetic and Potential energy of the UAV are established. Finally, a matrix is obtained by the concept of matrix direct product and the product of this matrix and the constraint matrix is a zero matrix. The Lagrange multipliers in the Lagrange’s equation are eliminated by the matrix, and the dynamics model of the UAV is established in modularization based on the Lagrange’s equation. In order to compare with the Lagrange’s equation, the Kane equation and ADAMS software are also used to establish a dynamics model of the UAV. The results show that the simulation of Lagrange’s equation, Kane equation and ADAMS software are basically the same, and the rationality of the dynamics modeling in this paper is verified.
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