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.

[3] 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.

[4] 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".

Chapter three discusses the integration of equations of motion at length, the conservation of energy and its role in reducing degrees of freedom, and separation of variables.

[9] Chapter fifteen, The General Theory of Orbits, describes two-dimensional mechanics of a particle subject to conservative forces and discusses special-case solutions of the Three-body problem.

A reviewer of the first edition noted that the book contains "the outlines of a long series of researches for which hitherto it has been necessary to consult English, French, German, and Italian transactions".

In 1980, Herbert Goldstein mentioned the book in his famous textbook Classical Mechanics where he noted that it was outdated, but remained a useful reference for some specialised topics.

[21][22] Lampe called the treatise an "excellent work" and states that Cambridge's treatment of analytical dynamics "has had, as a consequence, that the English student is directed with great energy towards the study of mechanics in which he displays excellent performance, as can be gauged from the many, and not at all easy, problems appended at the end of each chapter of this book.

[16][17] Bryan opens the review by writing that, though he is not does not care for the "University Presses competing with private firms", he believes "there can only be one opinion as to the series of standard treatises on higher mathematics emanating at the present time from Cambridge".

"[16][17] He went on to write: "We may take it as certain that the present volumes will be keenly read in Germany and America, and will be taken as proofs that England contains good mathematicians.

[23] The main actors in the polemic, other than Whittaker and Bryan, are an anonymous professor referred to only as "An Old Average College Don", Alfred Barnard Basset, Edward Routh, and Charles Baron Clarke.

The controversy revolved around Bryan's claim that many of the problems included in the book are "fictitious", similar to those used in the Cambridge Tripos examinations.

[29] Charles Baron Clarke insinuates that he is the "Old Average College Don" that wrote the first anonymous letter, and again emphasises his original complaint.

[34][23] After discussing more about aeroplanes and the development of their dynamics, Bryan closes the review by stating that the book "will be found of much use by such students of a future generation as are able to find time to extend their study of particle and rigid dynamics outside the requirements of aerial navigation"[34][23] and that it would serve as "a valuable source of information for those who are in search of new material of a theoretical character which they can take over and apply to any particular class of investigation.

"[34][23] George David Birkhoff wrote a review in 1920 stating that the book is "invaluable as a condensed and suggestive presentation of the formal side of analytical dynamics".

"[10] On chapter sixteen, also newly rewritten, he commented further that in treating the formal solutions for Hamiltonian systems using trigonometric series, the third edition replaced the method used in previous editions with a new one published by Whittaker in 1916 which Cherry states "must be regarded as suggestive rather than conclusive", noting that not all applicable proofs are included.

[37] Another reviewer of the final edition noted that the discussion of the three-body problem is brief and advanced such that it "will be difficult reading for one not already acquainted with the subject"[12] and that the references to then-recent American articles were incomplete, pointing to specific examples relating to the stability of the equilateral triangle positions for three finite masses.

[2] However, he criticised the book for having no diagrams, which harmed the sections on topics such as the Euler angles, tendency to make things more complicated than necessary, refusal to use vector notation, and "pedantic" problems of the kind found on the Cambridge Tripos examination.

[2][39] Despite the book's problems and its need to be updated, he went on to write: "It remains, however, a practically unique source for the discussion of many specialized topics.

"[2][39] The book quickly became a classic textbook in its subject and is said to have "remarkable longevity", having remained in print almost continuously since its initial release over a hundred years ago.

[41] During the 1910s, Albert Einstein was working on his general theory of relativity when he contacted Constantin Carathéodory asking for clarifications on the Hamilton–Jacobi equation and canonical transformations.

Soon he realised that the key idea in Heisenberg's paper was the anti-commutativity of dynamical variables and remembered that the analogous mathematical construction in classical mechanics was Poisson brackets.

[45][39] The treatise has remained in print for more than a hundred years, with four editions, a 1989 reprint with a new foreword by William Hunter McCrea, and translations in German and Russian.