穩定性分析是彈箭設計工作中重要的一環。在非線性氣動力特性下，線性穩定理論將變成無效。本研究的目的，即在建立彈箭角運動分析之非線性模式與探討其動態行為。
研究中首先推導出統御彈箭角運動之無因次方程組，其中氣動力導數如靜穩定、氣動力阻尼與延滯和Magnus力矩導數被考慮為姿態角函數關係。由四階Runge-Kutta方法可以得到攻角與側滑角隨時間的演化。同時利用相位圖、功率頻譜與水瀑圖做為分析系統動態行為之工具。藉由觀察特定彈箭，發現在某些情況下具有非線性氣動力導數下的結果與線性分析不同。角運動頻率受無因次轉速之影響甚鉅，而其它參數之影響則極微。

The flight stability analysis is very important in design of projectiles. As for nonlinear aerodynamic characteristics of the projectiles, the linear theory may become invalid. The objective of the present work is to build a nonlinear model for analysis of the angular motion and the dynamic behaviors of projectiles.
In the present study, firstly, a non-dimensionalized set of equations for governing the angular motion of projectiles is developed. To account for the nonlinearities of the system, the involved aerodynamic derivatives, i.e. static stability, aerodynamic damping and lagging, and Magnus moment derivatives are considered as functions of attitude angles. Time evolutions of angle-of-attack and side-slipping angle are obtained by solving nonlinear equations by using forth-order Runge-Kutta scheme. Phase diagrams, power spectra and water-fall diagrams are used as tools for analysis of dynamic behaviors of the system. By investigating a typical projectile, it is found that the results with the nonlinear aerodynamic derivatives may be different from those in the linear analysis at some conditions. The frequencies of the angular motion are strongly influenced by a dimensionless spin rate, while the other parameters only have little effects.

1. 前言
1.1. 研究動機
1.2. 文獻回顧
1.3. 研究重點
2. 數學模式
2. 1. 問題敘述與假設條件
2.2. 方程式推導
2.3. 角運動方程組之無因次化
2.4. 系統平衡解
2.5. 力矩係數導數與攻角、側滑角之關係
3. 數值計算
4. 非線性動態系統分析法
4.1 動態系統
4.2 動態系統穩定性
4.3 非線性動態行為分析
5. 結果與討論
5.1. 無因次轉速 對彈箭角運動的影響
5.2. 轉動慣量對飛行穩定性的影響
5.3. 密度比 對飛行穩定的影響
5.4. 尾翼裝置角 效應
5.5. 非線性俯仰力矩對彈箭穩定性的效應
5.6. 非線性Magnus力矩對彈箭穩定性之效應
5.7. 非線性阻尼力矩對彈箭飛行的影響
5.8. 非線性俯仰力矩、Magnus力矩、阻尼力矩對彈箭飛行影響
5.9 影響彈體角運動頻率的因素
6. 結論
參考文獻
自傳

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