摩擦係數對於在空氣中做旋轉運動的橢圓球體之影響

本文主要是在討論橢圓球體在空氣中做旋轉運動，利用改變空氣與橢圓球體摩擦係數，來觀察橢圓球體從水平面到垂直面運動情形。首先，利用Lagrange equations來求出橢圓球體在空氣中運動方程式。之後，在將運動方程式跟4階藍吉-庫塔法結合來求解不同摩擦係數下橢圓球體轉動軸的方向，由水平橫躺轉換至站立情形，進而找出前述運動不會發生，的摩擦係數所在的區間。根據數值模擬結果，由3個不同Euler's角得知橢圓球體相對位置，從角度變化可以觀察到橢圓球體運動情形及摩擦係數與其他關連性。

關鍵字

轉動軸；水平面；關連性；方程式

並列摘要

This thesis is discussing the oval spheroid and making rotatory sports in the air mainly, utilize and change the air and oval coefficient of friction of spheroid , the situation that to observe the oval spheroid and move from horizontal plane to vertical plane. First of all, make use of Lagrange equations to ask out the oval equation preface of the movement in the air of spheroid. Later , move equation preface with four order Runge-Kutta method solve different coefficient of friction oval spheroid rotate direction of axle to ask to come to combine, move crosswise lying and change it to the situation of standing by competence, and then will not take place to find out above-mentioned sports, coefficient of friction belong to block. Learnt the oval relative position of spheroid by three different Euler's angles according to the numerical simulation result, is it can observe oval spheroid sport situation and coefficient of friction and imprison of connecting from angle with while being other to change.

並列關鍵字

Lagrange ； Runge-Kutta

參考文獻

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國際替代計量

摩擦係數對於在空氣中做旋轉運動的橢圓球體之影響

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