|
カジヤマ ユウジ
Yuji Kajiyama
梶山 裕二 所属 教育学部 職種 准教授 |
|
| 言語種別 | 英語 |
| 発行・発表の年月 | 2021/06 |
| 形態種別 | 研究論文 |
| 査読 | 査読あり |
| 標題 | Explicit Calculation of Principle of Least Action |
| 執筆形態 | 単著 |
| 掲載誌名 | ACTA PHYSICA POLONICA A |
| 掲載区分 | 国外 |
| 出版社・発行元 | POLISH ACADEMY OF SCIENCE, INSTITUTE OF PHYSICS |
| 巻・号・頁 | 139(6),pp.704-709 |
| 総ページ数 | 6 |
| 概要 | In the standard way of analytical mechanics, the Euler–Lagrange equation as an equation of motion is derived from the principle of least action based on the variational principle. In this paper, we present an alternative way to describe the motion by explicitly solving an extreme value problem of the action without the variational principle. We assume that the position x(t) is expressed by power series of time t with an infinite number of unknown coefficients, and show that these coefficients can be correctly determined by the boundary conditions and the extremum conditions of the action by explicit calculations, which describe the actual motion. We will present the motion of a free particle, the motion under constant gravity, a harmonic oscillation, the time-dependent Lagrangian, and a non-linear force as examples. |