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：本文提出了一种面向机器人学、在SO(3)上无坐标的固定翼飞机逆飞行动力学表述。平移力平衡在世界坐标系中描述，旋转动力学在机体坐标系中描述；气动力方向（阻力、升力、侧力）通过几何方式定义，避免了局部姿态坐标的使用。通过施加协调飞行条件（无侧滑），我们推导出一个闭式轨迹到输入的映射，该映射可输出姿态、角速度以及推力-迎角对，并以分量形式恢复气动力矩系数。将此映射应用于球面平行线上的系留飞行，我们得到了所需滚转角的解析表达式，并识别出一个特定的零滚转轨迹，在该轨迹上系绳张力恰好平衡离心效应，从而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/阻力定律下，最小推力迎角具有闭式解。当轨迹与旋转动力学时不变时，这些逐点准稳态逆解即成为稳态飞行的配平状态。该框架将航空领域的逆仿真与机器人学中的几何建模相结合，为轨迹设计与可行性验证提供了一个严谨的基础模块。