A Treatise on the Analytical Dynamics of Particles and Rigid Bodies is a treatise and textbook on analytical dynamics by British mathematician Sir Edmund Taylor Whittaker. Initially published in 1904 by the Cambridge University Press, the book focuses heavily on the three-body problem and has since gone through four editions and has been translated to German and Russian. Considered a landmark book in English mathematics and physics, the treatise presented what was the state-of-the-art at the time of publication and, remaining in print for more than a hundred years, it is considered a classic textbook in the subject. In addition to the original editions published in 1904, 1917, 1927, and 1937, a reprint of the fourth edition was released in 1989 with a new foreword by William Hunter McCrea.
The book was very successful and received many positive reviews. A 2014 "biography" of the book's development wrote that it had "remarkable longevity" and noted that the book remains more than historically influential. Among many others, G. H. Bryan, E. B. Wilson, P. Jourdain, G. D. Birkhoff, T. M. Cherry, and R. Thiele have reviewed the book. The 1904 review of the first edition by G. H. Bryan, who wrote reviews for the first two editions, sparked controversy among Cambridge University professors related to the use of Cambridge Tripos problems in textbooks. The book is mentioned in other textbooks as well, including Classical Mechanics, where Herbert Goldstein argued in 1980 that, although the book is outdated, it remains "a practically unique source for the discussion of many specialized topics."
Background
Whittaker was 31 years old and working as a lecturer at Trinity College, Cambridge when the book was first published, less than ten years after he graduated from Cambridge University in 1895. Whittaker was branded Second Wrangler in his Cambridge Tripos examination upon graduation in 1895 and elected as a Fellow of Trinity College, Cambridge the next year, where he remained as a lecturer until 1906. Whittaker published his first major work, the celebrated mathematics textbook A Course of Modern Analysis, in 1902, just two years before Analytical Dynamics. Following the success of these works, Whittaker was appointed Royal Astronomer of Ireland in 1906, which came with the role of Andrews Professor of Astronomy at Trinity College, Dublin.
The second half of the treatise is an expanded version of a report Whittaker completed on the three-body problem at the turn of the century at the request of the British Science Association (then called the British Association for the Advancement of Science). In 1898, the council of the British Association passed a resolution that "Mr E. T. Whittaker be requested to draw up a report on the planetary theory". A year later, Whittaker delivered his report, titled “Report on the progress of the solution of the problem of three bodies”, in a lecture to the Association, who published it in 1900. He changed the name from the original "report on the planetary theory" to, in his own words, show "more definitely the aim of the Report", which covered the advances in theoretical astronomy that occurred between 1868 and 1898.
Content
The book is a thorough treatment of analytical dynamics, covering topics in Hamiltonian mechanics and celestial mechanics and the three-body problem. It has been noted that the book can be divided naturally into two parts: Part one, consisting of the twelve chapters, covers the basic principles of dynamics, giving a "state-of-the-art introduction to the principles of dynamics as they stood in the first years of the twentieth century", while part two, consisting of the final four chapters, is based on Whittaker's report on the three-body problem. While the first part remained mostly constant throughout the book's multiple editions, the second part was expanded considerably in the second and third editions.