Classical Mechanics and Chaos - Japanese Translation / 古典力学とカオス
Hardcover
General MathematicsGeneral Science
Publisher: Golden Tao Publishing
Published: Aug 28 2026
Pages: 416
Weight: 1.59
Height: 0.94 Width: 6.00 Depth: 9.00
Language: Japanese
This is the Japanese 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.
これは英語の原文からの翻訳です。
本書は、点粒子の運動に関する古典的な定式化から始めて、古典力学を解説します。古典力学が確立されて初めて、多くのシステムにおける運動には非カオス的領域とカオス的領域という2つの領域が存在することが認識されました。本書は、カオス理論を含む現代的な古典力学の解説であり、後の理論的発展との関連性も示しています。解説全体を通して、興味深い問題が提示され、その多くは解答付きで、残りは読者に委ねられています。これらの問題は、カリフォルニア工科大学、オックスフォード大学、ウィスコンシン大学で開講された古典力学と数学の講義から抜粋したものです。講義は学部レベルから大学院上級レベルまで多岐にわたります。ご想像のとおり、これらの講義では、豊富で洗練された教科書や参考資料が用いられており、本書でも同様にそれらの参考資料が活用されています。本書を進めていくと、摩擦力を加えるなどして、より複雑な振り子の運動に対応する、複雑さが増していく常微分方程式を効果的に学習していることがわかります。常微分方程式の基礎となる数学との強い整合性から、応用数学の観点から常微分方程式を簡単に復習するための付録を設けることにした。
本書は、カオスを含む基礎となる常微分方程式理論の現代的な解説に加え、古典力学理論が量子力学や特
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