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phs_17_045.pdf | 351.41 kB | Adobe PDF | 見る/開く |
タイトル: | <寄稿論文>紐でつるされた剛体の振動問題に関するLeonhard Eulerの解法の変遷 |
その他のタイトル: | <Memorial Articles>Transition of Leonhard Euler's Solutions about Vibration of a Rigid Body Suspended by a String |
著者: | 中田, 良一 |
著者名の別形: | NAKATA, Ryoichi |
発行日: | 31-Mar-2023 |
出版者: | 京都大学文学部科学哲学科学史研究室 |
誌名: | 科学哲学科学史研究 |
巻: | 17 |
開始ページ: | 45 |
終了ページ: | 64 |
抄録: | As an example of the establishment of the theory of motion of a rigid body suspended by a string, Leonhard Euler's three solutions, written in 1740, 1742 and 1773, are described. The first and second solutions deal only with small oscillations and give the equivalent simple pendulum length of the system from the balance of moments of force. The third solution, on the other hand, takes a Cartesian coordinate system and decomposes the motion of the system into translational motion of the center of gravity and rotational motion around the center of gravity. He applies the equations of motion (Newton's second law) to the former and the formula for rotational motion around a fixed point to the latter. He declares that these formulae are derived from first principles of mechanics, solves the differential equations for small oscillations and then expresses the motion of the system as a normal combination of two types of oscillation. He declares that by this dynamical method, problems of this kind can be solved completely in mechanics, even if the oscillations are not infinitely small. |
DOI: | 10.14989/286704 |
URI: | http://hdl.handle.net/2433/286704 |
出現コレクション: | 第17号 <伊藤先生追悼特集号> |
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