Professor Nivaldo A. Lemos takes part in a Q&A
Question: What inspired your book, Analytical Mechanics?
Answer: The original edition of the book was inspired by the need for an analytical mechanics textbook in Portuguese for advanced undergraduate and graduate students. The book’s favourable reception prompted me to engage in the preparation of a second edition. I then met with Simon Capelin (Editorial Director, Physics) who told me about Cambridge University Press’ interest in an English translation.
The tenor of the original edition is retained in the present English translation, seeking to join the traditional with the contemporary. Many fully worked-out examples make the book accessible to typical students. At the same time, the text intends to be stimulating and challenging to the most gifted students. The bibliography, which contains very advanced books and recent research papers, aims to excite the reader’s curiosity and show that classical mechanics is neither a museum piece nor a closed chapter of physics.
Besides a thorough revision of the original text, the main difference from the original Portuguese edition lies in the addition of several advanced topics, such as: a rigorous proof that action is least if the time interval is short enough; Frobenius integrability condition and basic theory of differential forms; quartic oscillator and Jacobi elliptic functions; canonical perturbation theory and introductory KAM theory; geometric phases; Poisson manifolds.
Q: What do you hope will be the lasting impact of this book?
A: It is hoped that, besides imparting the fundamental notions of analytical mechanics to fill the needs of most students, the book may prepare and persuade some readers to immerse themselves more deeply in, what I believe to be, a beautiful subject.
Q: What is your favourite historical anecdote included in your book?
A: The first variational principle in mechanics was put forward by Maupertuis, in 1744, in an obscure form marked by the intention of providing not only a rational, but also a theological basis to mechanics as proof of God’s power and wisdom. Maupertuis’ principle gained a definite and mathematically rigorous formulation, thanks to the efforts of Euler and Lagrange. Originally, it was given the name of “principle of least action” but this appellation is nowadays reserved by virtually all physicists to Hamilton’s principle.
Mathematician and astronomer, Pierre-Louis Moreau de Maupertuis was a member of the Paris Academy of Sciences, championed Newton’s gravitational theory in France, led an expedition to Lapland for measurements that confirmed the flattening of the Earth at the poles, became a member of the Berlin Academy of Sciences (which he presided from 1745 to 1753) and came to be called “Sir Isaac Maupertuis” by Voltaire. He was unjustly accused by the German mathematician Samuel König of having plagiarised Leibniz. In the priority dispute surrounding the then called “principle of least action”, Maupertuis was supported by no one less than Leonhard Euler, but Voltaire, his former admirer, turned against him and satirised the “Earth flattener” mercilessly. With failing health, Maupertuis did not withstand the pressure and abandoned Berlin in 1753.
Q: What topical events have illustrated the real world applications of your research?
A: The Kolmogorov-Arnold Moser theory, which is given an introductory description in Chapter 10, is closely connected with the question of the stability of the Solar System. It is also relevant to the recent discovery of chaotic behaviour in the Solar System.
Q: Can you summarize your new book and its audience?
A: The text fully covers the standard themes of an upper-level undergraduate course in analytical mechanics, such as Lagrangian and Hamiltonian dynamics, variational principles, rigid-body dynamics, small oscillations, canonical transformations, and Hamilton-Jacobi theory. It also addresses a significant number of advanced topics that make the book suitable for a graduate course.