Mechanics (Q2863024)

The book which is written in French is the second version of a series of lectures given by the author at EPFL in Lausanne. The modifications which have been done from the first version published in 2009 [\textit{J.-P. Ansermet}, Mécanique. Traité de Physique. Lausanne: Presses Polytechniques et Universitaires Romandes (2009; Zbl 1204.70001)] follow the creation of a MOOC on mechanics at EPFL. The book is divided in six chapters, four of them being devoted to the description of the bases of mechanics, illustrated with many examples, and the two last ones gathering problems and exercises. Each of the four first chapters start with a short description of the objectives, following a pedagogical presentation. Each chapter contains many figures and the main ideas or tools which are developed are highlighted in blue. A long bibliography ends the book.NEWLINENEWLINEIn Chapter 1, the author presents a complete review of the bases of mechanics. He starts with the kinematics of material points. The description of the two first laws of Newton is done, then that of action and reaction. The author moves to the description of dynamics for a point. He describes the normal and tangential accelerations and the rotations which lead to Poisson's formula. The notions of energy, power and work, of potential associated to a force and of potential energy are briefly described. The kinematics of a system of points are presented, before the dynamics of a solid. The chapter ends with a short presentation of the relativity, of Einstein's relativity principles and of the relativistic kinematics or dynamics. In 70 pages, the author thus gathers the main ideas and tools of the classical or relativistic kinematics or dynamics of points or solids.NEWLINENEWLINEChapter 2 is devoted to the description of different classical situations involving mechanical systems. In each case, the author builds an appropriate methodology which allows to derive the equations which governs the motion of this system and which solves these equations. The chapter starts with the study of ballistics with or without air resistance. It goes on with the harmonic oscillator damped or not, the plane pendulum, the inclined mass with friction\dots. Each situation leads to the presentation of connected notions: differential equations, velocity and acceleration in generalized coordinates, resonance, elastic or inelastic collisions, gravitation law, Newton's laws, motion on earth, conservation principles, inertia, momentum, Lorentz transformations\dots.NEWLINENEWLINEChapter 3 presents some historical and technical descriptions. After a short presentation of the ideas developed by the Greek scientists and by Galilei, the author presents a review of some questions which have been raised during the last centuries, starting from Newton's ideas and concerning gravitation, mass, chaos,\dots. He explains the concepts of field, of symmetry of tensor\dots.NEWLINENEWLINEThe Chapter 4 gathers the main tools of Lagrange's formalism. Once the author has derived the Lagrange equations in an abstract setting, he describes and studies several examples. The chapter ends with a short description of variational principles, illustrated with examples.NEWLINENEWLINEChapters 5 and 6 gather different problems with detailed corrections and exercises with short answers.NEWLINENEWLINEThroughout the whole book, the author takes a great care to introduce the concepts which are to be discussed and the tools which are developed and illustrated with different examples. Even if it is written in French, I am sure that it will help many students to understand the bases of mechanics from the classical concepts to the relativistic ones.