考虑刚体运动与弹体变形耦合效应的旋转导弹动力学建模

旋转导弹结构细长，具有较大弹性，结构低频振动易与刚体运动相互耦合。为更好地研究旋转导弹的动力学特性，对考虑刚体运动与弹体变形耦合效应的旋转导弹动力学建模问题展开研究。引入瞬态坐标系，在该坐标系下利用拉格朗日方程建立弹性旋转导弹的惯性耦合完整模型。该模型考虑了弹性变形对质量特性的影响，能够完整描述刚体运动和弹性变形间的耦合效应。在不同假设下，将惯性耦合完整模型简化后可得到弹性耦合简化模型和非惯性耦合模型。仿真分析结果表明：相对于其他两种简化模型，惯性耦合完整模型能够更全面地描述旋转导弹的运动，而刚体运动与弹体变形耦合效应在旋转导弹建模和分析中不可忽略，需要加以考虑；在旋转导弹运动稳定情况下，3种模型的差别主要体现在姿态运动上，而在弹性变形上的差别可以忽略。

Dynamics Modeling of Spinning Missiles Considering the Rigid-elastic Coupling Effect

Considering the interaction between flexible and rigid modes caused by the increased aspect ratio and elasticity of spinning missile, the nonlinear equations of motion for elastic spinning missile are developed. The transient coordinate system, in which vibration mode is used to describe the missile’s elastic deformation, is introduced. The slice theory is used to establish an aerodynamics model. Lagrangian equation is used to derive the complete inertial coupling model of elastic spinning missiles. In the model, the influence of elastic deformation on the mass property is considered, and the coupling effect between flexible and rigid modes are fully described. Under different assumptions, the complete inertial coupling model can be simplified to obtain the simplified inertial and non-inertial coupling models. Numerical simulations demonstrate that the main difference on the attitude motion is not negligible, while the difference on the flexible mode is negligible. The influence of inertial coupling must be considered in the modeling and analysis of elastic spinning missile.