Classical Mechanics and Chaos - Chinese Traditional Translation / 經典力學與混沌: Book 1 of Physics from Max
Hardcover
General MathematicsGeneral Science
Publisher: Golden Tao Publishing
Published: Aug 28 2026
Pages: 368
Weight: 1.45
Height: 0.81 Width: 6.00 Depth: 9.00
Language: Chinese
This is a Chinese Traditional translation from the English original.
This book provides a description of classical mechanics, starting with the classic formulations of point particle motion. It wasn't until classical mechanics was already well established that it was realized that there are two domains for motion in many systems: non-chaotic; and chaotic. This is a modern exposition of classical mechanics, thus including chaos theory, and including ties to later theoretical developments as well. The exposition consists, throughout, of the presentation of interesting problems with many solved, the others left for the reader. The problems are drawn from classical mechanics and mathematics courses taken at Caltech, Oxford, and the University of Wisconsin. The courses range from undergraduate level to advanced graduate level. The courses had a rich and sophisticated selection of textbook and reference material, as you might expect, and those reference texts are, similarly, drawn on here. As we progress through the material we will see that we are effectively studying ordinary differential equations of increasing complexity (corresponding to more complicated pendulum motion, for example, such as by adding a frictional force). This strong alignment with the underlying mathematics of ordinary differential equations motivates the placement of an appendix for a quick review of ordinary differential equations from the applied mathematics perspective.
In addition to a modern exposition of the underlying ordinary differential equation theory, with chaos included, the other main modern elements are to indicate where the classical mechanics theory can bridge into the theories yet to come, such as quantum mechanics and Special Relativity. There are five theoretical implementation areas of Classical Mechanics where Quantum Mechanics is trivially indicated (by analytic extension/continuation, or by algebraic modification from abelian to non-abelian), and such areas are described in detail. Similarly, there are three areas of experimental application where Special Relativity is indicated, that are also described.
這是從英文原文翻譯而來。
本書從經典質點運動的經典公式著手,對經典力學進行了闡述。直到經典力學體系發展成熟後,人們才意識到許多系統中的運動存在兩個領域:非混沌運動和混沌運動。本書是經典力學的現代詮釋,因此涵蓋了混沌理論,並與後來的理論發展有所關聯。全書貫穿始終地呈現了一些有趣的習題,其中許多習題已得到解答,其餘的則留給讀者自行探索。這些習題皆取材自作者在加州理工學院、牛津大學和威斯康辛大學修讀的經典力學和數學課程,課程難度涵蓋大學部到研究生各個階段。正如您所料,這些課程使用了豐富而精深的教材和參考資料,本書也同樣借鑒了這些參考書。隨著學習的深入,我們將發現,我們實際上是在研究越來越複雜的常微分方程式(例如,對應於更複雜的擺運動,例如透過添加摩擦)。由於與常微分方程的基本數學原理高度契合,因此我們特意添加了一個附錄,從應用數學的角度對常微分方程進行快速回顧。
除了對包含混沌在內的基本常微分方程理論進行現代闡述之外,其他主要現代內容還在於指出經典力學理論如何與量子力學和狹義相對論等未來理論相銜接。經典力學的五個理論應用領域可以很容易地與量子
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