A Well-Known Book
I first heard of this book—Sur le problème des trois corps et les équations de la dynamique by Henri Poincaré—around 1978 or around 1982. I no longer remember the particular time or context although there are a few conceivable possibilities.
At that time, I was in an environment that recognized, respected and understood (on some level) the importance of this book. And it did so despite 2 obstacles. The first was of course its age; it was published in 1890. The other obstacle, from the perspective of a US academic environment, was the language; it was written in formal French with a specialized vocabulary demanded by the subject matter. In 1982, I spoke French that was fully adequate for many purposes; yet it then seemed to me unlikely that I would be able to read and understand Poincaré’s work, so I made no effort to try.
Together, this means that the book was a classic and inaccessible to a large readership even though its existence was well known. By translating it into English, I’ve made it more accessible.
An Important Work
This work was well known for two main reasons.
First, it is a break from previous efforts to understand the motion of the planets in the solar system and also (for example) the Lunar Problem—the motion of the sun, earth and moon. Their motion is determined by Newton’s three laws of motion and Newton’s law of gravitation. Before Poincaré the effort had focused on calculations and methods for calculating the planetary positions. Instead, Poincaré looked at the differential equations arising from Newton’s laws and worked on understanding the general properties of the solutions by studying the equations themselves.
Second, and now switching to the second half of the title, Poincaré studied these equations in their Hamiltonian form. (This is what Poincaré meant by canonical equations of dynamics.) This gave his results and approach great generality and introduced important tools like Poincaré maps, the recurrence theorem and phase space trajectories.
My Translation…
A key consideration in preparing this translation was accessibility. In that way, my purpose for the translation is the scholarly presentation of Poincaré’s ideas and approach to studying and understanding dynamical systems and particularly the general three-body problem.
To support that, I paid particular attention to make sure that Poincaré’s voice came through clearly. I tried to avoid retelling in my words what Poincaré had written and followed closely what and how Poincaré wrote.
I also put great effort into accuracy: carefully verifying the terminology, confirming consistency in its use and carefully checking the result.
… Becomes My First Book
In December 2016 I completed the translation that I started in March 2014 and signed a publication contract.
It was published in May 2017 by Springer. For more information see: Springer catalog entry. It is also available from Amazon.