古典力學專題之研討

Abstract

我們可以利用微分流形的概念描述一個受到穩定且完整約束的運動系統 並且可在標圖上定義若干個獨立座標利用Lagrange equation去求解當然有關微小震動,以及剛體運動所產生的若干性質,是在討論的範圍之內最後則是觀察陀螺的主軸在一些特定條件之下於空間中的運動型態

We can use the concept of the differentiable manifold to express a system with an ideal holonomic constraint, and we can define the generalized coordinate on a chart of an atlas of the manifold. So we can solve it by Lagrange equation. Of course we will study some topics in mechanics like small oscillation, the motion of a rigid body. Finally, we will investigate of sleeping and fast tops even of the case that in the absence of gravity.