<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

Abstract

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.