We present a robotics-oriented, coordinate-free formulation of inverse flight dynamics for fixed-wing aircraft on SO(3). Translational force balance is written in the world frame and rotational dynamics in the body frame; aerodynamic directions (drag, lift, side) are defined geometrically, avoiding local attitude coordinates. Enforcing coordinated flight (no sideslip), we derive a closed-form trajectory-to-input map yielding the attitude, angular velocity, and thrust-angle-of-attack pair, and we recover the aerodynamic moment coefficients component-wise. Applying such a map to tethered flight on spherical parallels, we obtain analytic expressions for the required bank angle and identify a specific zero-bank locus where the tether tension exactly balances centrifugal effects, highlighting the decoupling between aerodynamic coordination and the apparent gravity vector. Under a simple lift/drag law, the minimal-thrust angle of attack admits a closed form. These pointwise quasi-steady inversion solutions become steady-flight trim when the trajectory and rotational dynamics are time-invariant. The framework bridges inverse simulation in aeronautics with geometric modeling in robotics, providing a rigorous building block for trajectory design and feasibility checks.

翻译：我们提出了一种面向机器人学的、基于SO(3)的无坐标形式固定翼飞行器逆飞行动力学建模方法。平动受力平衡在世界坐标系中建立，而旋转动力学则在机体坐标系中描述；气动方向（阻力、升力、侧力）通过几何方式定义，避免使用局部姿态坐标。在强制协调飞行（无侧滑）条件下，我们推导出从轨迹到输入的闭式映射，从而获得姿态、角速度以及推力-迎角组合，并逐项恢复气动力矩系数。将该映射应用于球面平行线上的系留飞行，我们得到了所需倾斜角的解析表达式，并识别出一个特定零倾斜角轨迹，在该轨迹上系绳张力恰好平衡离心效应，凸显了气动协调与表观重力矢量之间的解耦特性。在简单的升力/阻力模型下，最小推力对应的迎角具有闭式解。当轨迹与旋转动力学为时不变时，这些逐点准稳态逆解退化为稳态飞行配平状态。该框架将航空领域的逆仿真与机器人领域的几何建模相衔接，为轨迹设计与可行性验证提供了严谨的基础工具。