Lectures in Classical Mechanics

Victor Ilisie, B.S., M.S., Ph.D., is a postdoctoral researcher at the Institute for Instrumentation in Molecular Imaging, Spanish National Research Council (CSIC) and associate professor at the University of Valencia (Spain). During his Ph.D., Dr. Ilisie's research focused on the study of high-energy physics phenomena related to the Large Hadron Collider (Geneva) and Higgs physics. Since then, his research activities have contributed to various fields in particle physics and medical physics, and he has also authored a book on quantum field theory. His skills and experience have been highly useful in developing projects related to PET, SPECT, and image reconstruction. Most of his postdoctoral research has focused on the study of high-resolution and high-sensitivity PET that incorporates the Compton effect, in a project financed by the European Research Council under the European Union's Horizon 2020 research and innovation program. He is also coordinating the development of a SPECTproject in a collaboration between Bruker Corporation and the Institute for Instrumentation in Molecular Imaging, and is involved in a project on the design and development of a novel multi-pinhole high-sensitivity SPECT device.

This exceptionally well-organized book uses solved problems and exercises to help readers understand the underlying concepts of classical mechanics; accordingly, many of the exercises included are of a conceptual rather than practical nature. A minimum of necessary background theory is presented, before readers are asked to solve the theoretical exercises. In this way, readers are effectively invited to discover concepts on their own. While more practical exercises are also included, they are always designed to introduce readers to something conceptually new.

Special emphasis is placed on important but often-neglected concepts such as symmetries and invariance, especially when introducing vector analysis in Cartesian and curvilinear coordinates. More difficult concepts, including non-inertial reference frames, rigid body motion, variable mass systems, basic tensorial algebra, and calculus, are covered in detail. The equations of motion in non-inertial reference systems are derived in two independent ways, and alternative deductions of the equations of motion for variable mass problems are presented. Lagrangian and Hamiltonian formulations of mechanics are studied for non-relativistic cases, and further concepts such as inertial reference frames and the equivalence principle are introduced and elaborated on.

Helps readers learn new concepts through illustrative exercises

Vector Analysis in Cartesian Coordinates.- Vector Analysis in Curvilinear Coordinates.- Kinematics.- Newton's Laws, Dynamics and Galilean Relativity.- Systems of Particles and Variable Mass.- One-Dimensional Potentials and Two-Dimensional Central Potentials.- Non Relativistic Collisions.- Continuous Mass Distributions. Gravitational Potential and Field.- Non-Inertial Reference Systems.- Rigid Body Dynamics.- Special Theory of Relativity.- Relativistic Collisions and Decays.- Non-Relativistic Lagrangian and Hamiltonian Mechanics.