現代運載火箭為提升酬載能力與飛行性能，逐漸朝高細長比、高推重比及輕量化發展，使箭體彎曲自然頻率降低，結構撓性更加顯著。液態推進劑占起飛總質量之相當比例，其持續消耗與桶槽內晃動亦使火箭的質量、慣性及流體參數隨時間改變。在推力與氣動擾動作用下，剛體運動、結構撓曲、推進劑晃動及引擎擺動會產生非線性時變耦合。因此，本研究旨在建立兼具時變物理參數與多體耦合效應之數值架構，探討結構、流體與控制系統間的交互影響。
本研究以Quasi-Lagrange方法推導火箭平移、旋轉、結構撓曲、推進劑晃動及推力向量控制（Thrust Vector Control, TVC）引擎擺動之二階非線性矩陣運動方程式；利用傳遞矩陣法計算隨推進劑消耗及級間分離而變化之自然頻率與模態函數，並結合SLOSH-ML取得時變等效晃動參數。模型整合於MATLAB/Simulink，建立由參數計算至受控飛行模擬之分析平台，並以Saturn V公開資料進行軌跡比對。本研究另比較剛體、純撓性、純晃動及全耦合模型，並建立不同細長比之Rocket A與Rocket B，分析其多體耦合特徵及控制增益敏感度。
結果顯示，模擬之高度、慣性速度及級間分離事件與Saturn V歷史資料具有一致的整體趨勢。相較於剛體模型，純晃動模型之TVC綜合擺角均方根值增加約13.0%，純撓性與全耦合模型則分別降低約25.9%與15.3%，顯示不同多體效應會改變控制器之擺角活動程度。Rocket A起飛初期之一階彎曲角頻率約為3.3 rad/s，Rocket B之三階角頻率約為42.4 rad/s。Rocket A之模態響應放大、TVC頻繁觸限及姿態角大幅變動，與撓性—噴嘴轉動耦合區塊量值較大的時段相互對應。控制增益分析顯示，Rocket A採用0.8倍增益時之最大高度約為219 km，較基準組提高約19.0%；Rocket B採用1.4倍增益時則約為178 km，提高約7.9%，呈現不同的增益敏感度。
綜合而言，火箭幾何構型不僅影響結構模態與推進劑晃動參數，也會改變多體耦合特徵與控制增益敏感度。本研究建立一套連結多體運動方程式、時變參數計算、受控飛行模擬與構型—控制比較之統一分析流程，並以量化指標呈現結構、流體與控制系統交互作用對飛行響應的影響，可作為後續結構—控制整合分析與控制器設計之基礎。

Modern launch vehicles increasingly adopt slender, lightweight, and high-thrust-to-weight designs, making structural flexibility more significant. Propellant depletion and sloshing also produce time-varying mass, inertia, and fluid parameters. Under thrust and aerodynamic disturbances, rigid-body motion, structural bending, propellant sloshing, and engine motion interact as a nonlinear, time-varying multibody system. This study develops a numerical framework to investigate these structural–fluid–control interactions.
Using the Quasi-Lagrange formulation, second-order nonlinear matrix equations are derived for vehicle translation, rotation, structural bending, propellant sloshing, and thrust vector control (TVC) engine gimbal motion. The Transfer Matrix Method and SLOSH-ML are used to obtain time-varying structural modes and equivalent slosh parameters. The models are implemented in MATLAB/Simulink and compared with public Saturn V trajectory data. Rigid-body, flexible-only, slosh-only, and fully coupled models are evaluated. Two configurations with different slenderness ratios, Rocket A and Rocket B, are also examined through multibody coupling and control-gain sensitivity analyses.
The simulated altitude, inertial velocity, and staging events follow the overall trends of the Saturn V data. Relative to the rigid-body model, the combined root-mean-square TVC gimbal angle increases by 13.0% for the slosh-only model, but decreases by 25.9% and 15.3% for the flexible-only and fully coupled models, respectively. Rocket A has an initial first bending-mode angular frequency of 3.3 rad/s, whereas Rocket B has a third-mode angular frequency of 42.4 rad/s. For Rocket A, modal amplification, frequent TVC saturation, and large attitude excursions coincide with an increased flexibility–nozzle coupling-block magnitude. With a gain factor of 0.8, Rocket A reaches a maximum altitude of 219 km, a 19.0% improvement over the baseline case. With a gain factor of 1.4, Rocket B reaches 178 km, a 7.9% improvement, demonstrating configuration-dependent gain sensitivity.
Vehicle geometry therefore affects structural modes, slosh parameters, multibody coupling, and control-gain sensitivity. The main contribution is a unified workflow connecting multibody equations, time-varying parameter calculation, controlled-flight simulation, and configuration-dependent control analysis, providing a foundation for integrated structure–control analysis and controller design.

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