查詢結果分析
來源資料
相關文獻
- Is the Inverse Square Law an Optimal Controller from Nature?What is the Action?
- 線性二次最佳調整器控制法於磁浮軸承之應用
- Nonlinear Optimal Vibration Suppression of Timoshenko beams Traversed by a Moving Mass
- 兼具反應與控制力限制之結構最佳控制
- 智慧型園圃自動澆灌控制系統
- 工農業生產過程中之環境類型風險損失的最佳控制策略
- 多軸轉向聯結車轉向控制--最佳控制
- Command Trajectory of Fast Forearm Movements Estimated by Optimal Control Theory
- On the Equivalence of Optimal Systems Design in the Time Domain and Frequency Domain
- On the Two-Degree-Of-Freedom Wiener-Hopf Optimal System Design
頁籤選單縮合
題 名 | Is the Inverse Square Law an Optimal Controller from Nature?What is the Action?=試問平方反比定律可否為大自然的最佳控制器?對應的行動能量為何? |
---|---|
作 者 | 黃皇男; 楊憲東; | 書刊名 | 東海科學 |
卷 期 | 4 2002.07[民91.07] |
頁 次 | 頁63-83 |
分類號 | 314.7 |
關鍵詞 | 平方反比定律; Lagrangian泛函; Pontryagin最小原則; 最佳控制; 反問題; Inverse square law; Lagrangian; Pontryagin minimal principle; Optimal control; Inverse problem; |
語 文 | 英文(English) |
中文摘要 | 於古典力學範畤,通常先設定某一Lagrangian泛函為系統的行動能量,再利用變分法求其最小值而決定該系統的運動方程式。倘若我們假定平方反比定律為大自然的最佳控制手段,試問其對的行動能量為何?本文以二個物體的平面運動為分析對象,來回答此一問題。首先利用Pontryagin最小原則,推導發現該行動能量須滿足特定的偏微分方程。此一方程的解雖有無限多組,然其中一組的解為該系統的行動能量是總能量,所顯示的物理意義為大自然若採平方反比定律為最佳控制器,其目的在維持物體沿特定軌道運動的總能量為固定。文章最後,將乙問題推廣到多體運動的情形,得到一組偏微分,在一般情形下不易求解。 |
英文摘要 | The usual way in developing the formulation for classical mechanics is to define the Lagrangian for the action first and then the equation of motion is obtained by using calculus of variation to minimize the action. If we recognize the inverse square law being an optimal controller presented by nature, what is the corresponding action (or Lagrangian) for it? First of all, a planar motion of two bodies is considered. An optimal control problem is then formulated with a presumed unknown Lagrangian. By using Pontryagin minimal principle to minimize the action, a partial differential equation for the Lagrangian is obtained and solved. For this action, it can be verified directly that the inverse square law is the corresponding optimal controller. Finally, the generalization of this mechanization is presented for more complicated dynamical systems. This type of problem is considered as an inverse problem from the optimal control theory point of view. |
本系統中英文摘要資訊取自各篇刊載內容。