Analytical Mechanics: Classical, Lagrangian and Hamiltonian Mechanics, Stability Theory, Special Relativity

Valter Moretti

touko 2023 · UNITEXT Kirja 150 · Springer Nature

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This textbook aims at introducing readers, primarily students enrolled in undergraduate Mathematics or Physics courses, to the topics and methods of classical Mathematical Physics, including Classical Mechanics, its Lagrangian and Hamiltonian formulations, Lyapunov stability, plus the Liouville theorem and the 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 is introduced in an axiomatic way, starting from a limited number of physical assumptions. Special attention is paid to themes with a major impact on Theoretical and Mathematical Physics beyond Analytical Mechanics, such as the Galilean symmetry of classical Dynamics and the Poincaré symmetry of relativistic Dynamics, the far-fetching relationship between symmetries and constants of motion, the coordinate-free nature of the underpinning mathematical objects, or the possibility of describing Dynamics in a global way while still working in local coordinates. Based on the author’s established teaching experience, the text was conceived to be flexible and thus adapt to different curricula and to the needs of a wide range of students and instructors.

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Valter Moretti is Full Professor of Mathematical Physics at University of Trento (Italy) and currently head of the doctoral school in mathematics. He is the coordinator of the research group in mathematical physics and of the local research group on quantum and quantum relativistic theories at Trento Institute for Fundamental Physics and Applications, within the Italian National Institute for Nuclear Physics. He is author/co-author of several books on quantum and quantum relativistic theories and has published over 70 papers in international journals on the subject, including quantum information. He is co-owner of an international patent on quantum technologies. He is member of the managing board of the interdepartmental Laboratory Quantum@TN on quantum sciences and technologies.

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