Ref.

Usually, engineering students know nothing about analytical mechanics except for a few students who decide to take analytical mechanics courses. The mainstream textbooks taught physics from a Newtonian approach, using mostly vectors and potentials. When the students encounter Lagrangians and Hamiltonians they usually don’t understand the intricate mathematical foundations behind them. Unfortunately, many aspects of interesting theoretical physics are forbidden for engineering students: phase and configuration space, Noether’s theorem, Poincare’s methods, relativistic equations, Feynman’s quantum-mechanical interpretation of the principle of least action, and so on. There are several interesting features of this book. It explains the differences between variation and differentiation, something that most books on the subject leapfrog. It explains clearly the D’Alembert Principle and the Principle of Virtual Work (Often omitted at the undergraduate level). From those principles the author derives the Principle of Least Action (Hamiltonian Principle), using just elemental calculus. Then he introduces the reader to Legendre’s transformation and the relations between the two fundamental quantities of analytical mechanics: Lagrangian and Hamiltonian. In addition, equations of movement corresponding to those quantities: Euler-Lagrange (Lagrangian) and canonical (Hamiltonian) equations, a powerful insight into configuration and phase spaces, including the wonderful Liouville’s theorem, and
the analogies between optics and mechanics (Snell’s law) when he explains the Hamilton-Jabobi equations.

I can say that this is a defacto compendium of variational principles that we engineers take for granted despite its intricate nature. Of course, I don’t think there are going to be that many students at Politecnico who are going to be interested in reading this kind of somewhat pedantic subject. But who knows? One that the student who reads this might save humanity.

s260250 AT studenti DOT polito DOT it