General mechanics: Solid dynamics: Course notes and corrected exercises for first-year mechanical engineering students

This course covers the fundamental concepts of mechanics, aimed primarily at students of mechanical engineering, with the aim of providing a thorough understanding of theoretical principles and their practical application. It covers key concepts such as mass analysis, kinetics, dynamics and energetics of material systems. The course begins with the geometry of masses, dealing with the center of mass, moment of inertia, and matrix of inertia, as well as fundamental theorems such as those of Guldin and Huygens. Next, the study of kinetics explains kinetic and dynamic torsors and their application to various systems. The Fundamental Principle of Dynamics (PFD) is explored, with particular emphasis on dynamic balancing to minimize vibrations. Finally, the energy section covers power, work, kinetic and potential energies. The course concludes with corrected problems to consolidate what has been learned through practical examples.