Softcover ISBN:  9781470456719 
Product Code:  HMATH/45 
List Price:  $120.00 
MAA Member Price:  $108.00 
AMS Member Price:  $96.00 
eBook ISBN:  9781470465087 
Product Code:  HMATH/45.E 
List Price:  $120.00 
MAA Member Price:  $108.00 
AMS Member Price:  $96.00 
Softcover ISBN:  9781470456719 
eBook: ISBN:  9781470465087 
Product Code:  HMATH/45.B 
List Price:  $240.00 $180.00 
MAA Member Price:  $216.00 $162.00 
AMS Member Price:  $192.00 $144.00 
Softcover ISBN:  9781470456719 
Product Code:  HMATH/45 
List Price:  $120.00 
MAA Member Price:  $108.00 
AMS Member Price:  $96.00 
eBook ISBN:  9781470465087 
Product Code:  HMATH/45.E 
List Price:  $120.00 
MAA Member Price:  $108.00 
AMS Member Price:  $96.00 
Softcover ISBN:  9781470456719 
eBook ISBN:  9781470465087 
Product Code:  HMATH/45.B 
List Price:  $240.00 $180.00 
MAA Member Price:  $216.00 $162.00 
AMS Member Price:  $192.00 $144.00 

Book DetailsHistory of MathematicsVolume: 45; 2021; 255 ppMSC: Primary 70; Secondary 01; 85
Owing to its simple formulation and intractable nature, along with its application to the lunar theory, the threebody 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 Poincaré, but also by others such as Sir George Darwin.
The book begins with a detailed description of the early history of the threebody problem and its periodic solutions, with chapters dedicated to the pioneering work of Hill, Poincaré, and Darwin. This is followed by the first indepth 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.
ReadershipGraduate students and researchers interested in the threebody problem and Forest Ray Moulton's work.

Table of Contents

Chapters

Introduction

The threebody problem and its first periodic solutions

Hill’s variational orbit

Poincaré’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


Additional Material

RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Requests
Owing to its simple formulation and intractable nature, along with its application to the lunar theory, the threebody 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 Poincaré, but also by others such as Sir George Darwin.
The book begins with a detailed description of the early history of the threebody problem and its periodic solutions, with chapters dedicated to the pioneering work of Hill, Poincaré, and Darwin. This is followed by the first indepth 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.
Graduate students and researchers interested in the threebody problem and Forest Ray Moulton's work.

Chapters

Introduction

The threebody problem and its first periodic solutions

Hill’s variational orbit

Poincaré’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