Analytical Mechanics

This textbook aims at introducing readers, primarily studentsenrolled in undergraduate Mathematics or Physics courses, to thetopics and methods of classical Mathematical Physics, including Classical Mechanics, itsLagrangian and Hamiltonian formulations, Lyapunovstability, plus the Liouville theorem andthe Poincaré recurrence theorem among others. The material also rigorously covers the theory of Special Relativity. The logical-mathematical structure of the physical theories of concern isintroduced in an axiomatic way, starting from a limitednumber of physical assumptions. Special attention is paid tothemes with a major impact on Theoretical and MathematicalPhysics beyond Analytical Mechanics, such as the Galilean symmetry of classical Dynamics and the Poincaré symmetry ofrelativistic Dynamics, the far-fetching relationship between symmetriesand constants of motion, the coordinate-free nature of the underpinning mathematical objects, or the possibility ofdescribing Dynamics in a global way while still working in localcoordinates. Based on the author's established teaching experience, the text was conceived to beflexible and thus adapt to different curricula and to the needs ofa wide range of students and instructors.