以相對運動法進行科氏效應之視覺化模擬

Visualized Simulation of Coriolis Effect Using Relative Motion Method

徐以帆(Yi-Fan Shyu) ； 谷岳峰(Yueh-Feng Ku) ； 曾靖夫(Jing-Fu Tseng)

《物理教育學刊》 21卷1期 (2020/07) Pp. 22-41

https://doi.org/10.6212/CPE.202007_21(1).0002

摘要

科氏效應是中學生較難以理解的古典力學觀念，因此本研究避開微積分的計算，僅利用慣性座標系中的牛頓運動定律，配合相對運動的觀念，以數值方法視覺化地模擬科氏效應。首先，於慣性座標系中計算物體運動，再將觀察者視角轉換至非慣性座標系中，即利用相對運動的觀念將物體運動投影至非慣性座標系，如此，不須計算假想力的作用，位於非慣性座標系中的觀察者即可直接觀察到科氏效應及各種假想力自然呈現。本研究以上述方法利用Python進行視覺化模擬，開發出四個模擬程式，包含平面上及球體上的假想力模擬，例如：地球上的長程砲彈及傅科擺之運動分析，避免了現實中實驗不易且通常只能進行小規模實驗的困難。本研究亦將此方法模擬之結果分別和真實數據及套用假想力公式計算之結果進行比較，以確認其正確性。另外，我們發現：教科書中對科氏效應影響地表氣旋的示意圖過度簡化，若教師補充說明不足，可能造成學生誤會。最後，本研究將模擬程式原始碼開放給有興趣的學生及教師，希望能幫助同學們理解科氏效應的概念。

關鍵字

科氏力 ； 相對運動 ； 假想力 ； 傅科擺 ； 電腦模擬

並列摘要

Coriolis effect is a relatively difficult concept in classical mechanics for high school students. Therefore, this research avoided calculus and used Newton's laws of motion in inertia coordinate system along with the concept of relative motion to simulate Coriolis effect in a visualized manner using numerical method. First, the object motion is calculated in an inertia coordinate system. Secondly, the observer is transferred into a non-inertia coordinate system. That is, the object motion is projected into a non-inertia coordinate system using the concept of relative motion. Therefore the observer in non-inertia coordinate system can observe the presentation of Coriolis effect and other fictitious forces without the calculation of the effect of fictitious force. Using the above method, this research employed Python to developed four visualized simulation programs, which include simulations of fictitious forces on both a plane and a sphere. For example, the motion analysis of long-range projectile and Foucault pendulum on Earth. With these simulation programs, the difficulties of conducting full-scale or reduced-scale experiments can be avoided. This research also compared the results of the presented method with experimental data and that from the equations of fictitious force to confirm its correctness. Besides, it is found that the demonstration of the influence of Coriolis effect on cyclone in high school textbooks is over-simplified and is likely to mislead students if their teacher does not explain in details. Finally, this research offered the source codes of the simulation programs to interested students or teachers and expects to help students to understand the concept of Coriolis effect.

並列關鍵字

computer simulation ； Coriolis effect ； fictitious force ； Foucault pendulum ； relative motion