Periodic orbits : F.R. Moulton's quest for a new lunar theory
著者
書誌事項
Periodic orbits : F.R. Moulton's quest for a new lunar theory
（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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