Rational Mechanics

This manual is a basic course in Physics 4, titled Rational Mechanics. It is part of the core curriculum for the 3rd semester of the common foundational program in the sciences and engineering field. It is intended for second-year undergraduate students (LMD system). This document adheres to the syllabus of Rational Mechanics for the fields of Civil Engineering, Mechanical Engineering, Public Works, Aeronautics, and Hydraulics, as taught at the Faculty of Technologies of Djillali Liabes University in Sidi Bel Abbès. It is written in the form of detailed lectures with solved applications. The content is organized into six chapters. The first chapter serves as a mathematical review aimed at providing students with the foundational knowledge required for understanding the course. It includes operations on vectors, moments, and torsors. The second chapter addresses the statics of rigid bodies. It introduces fundamental concepts in statics, such as material points, perfect rigid bodies, forces, moments, wrenches, the equilibrium of force systems, constraints, reactions, operations on forces, and the equilibrium of solids in the presence of friction.