Periodic orbits : F.R. Moulton's quest for a new lunar theory

書誌事項

Periodic orbits : F.R. Moulton's quest for a new lunar theory

Craig A. Stephenson

(History of mathematics, v. 45)

American Mathematical Society, c2021

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注記

"Applied mathematics"--Cover

Includes bibliographical references (p. 227-247) and indexes

内容説明・目次

内容説明

Owing to its simple formulation and intractable nature, along with its application to the lunar theory, the three-body problem has since it was first studied by Newton in the Principia attracted the attention of many of the world's most gifted mathematicians and astronomers. Two of these, Euler and Lagrange, discovered the problem's first periodic solutions. However, it was not until Hill's discovery in the late 1870s of the variational orbit that the importance of the periodic solutions was fully recognized, most notably by Poincare, but also by others such as Sir George Darwin. The book begins with a detailed description of the early history of the three-body problem and its periodic solutions, with chapters dedicated to the pioneering work of Hill, Poincare, and Darwin. This is followed by the first in-depth account of the contribution to the subject by the mathematical astronomer Forest Ray Moulton and his research students at the University of Chicago. The author reveals how Moulton's Periodic Orbits, published in 1920 and running to some 500 pages, arose from Moulton's ambitious goal of creating an entirely new lunar theory. The methods Moulton developed in the pursuit of this goal are described and an examination is made of both the reception of his work and his legacy for future generations of researchers.

目次

Introduction The three-body problem and its first periodic solutions Hill's variational orbit Poincare's research on periodic orbits Darwin's numerical search for periodic orbits Forest Ray Moulton Moulton's mathematical methods Oscillating satellites A new lunar theory Moulton's Periodic Orbits Epilogue Appendix A: Moulton's doctoral students Appendix B: Letters Appendix C: The Moulton plane Appendix D: Glossary Bibliography Name index Subject Index

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