Analytical Mechanics

This textbook aims at introducing readers, primarily studentsáenrolled in undergraduate Mathematics or Physics courses, to theátopics and methods of classical Mathematical Physics, including Classical Mechanics, itsáLagrangian and Hamiltonian formulations, Lyapunovástability, plus the Liouville theorem andáthe 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 isáintroduced in an axiomatic way, starting from a limitedánumber of physical assumptions. Special attention is paid toáthemes with a major impact on Theoretical and MathematicaláPhysics beyond Analytical Mechanics, such as the Galilean symmetry of classical Dynamics and the Poincaré symmetry ofárelativistic Dynamics, the far-fetching relationship between symmetriesáand constants of motion, the coordinate-free nature of the underpinning mathematical objects, or the possibility ofádescribing Dynamics in a global way while still working in localácoordinates. Based on the authorâÇÖs established teaching experience, the text was conceived to beáflexible and thus adapt to different curricula and to the needs ofáa wide range of students and instructors.