Analytical Mechanics

This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates.

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.

Authors: Helrich, Carl S.
Leaps directly into the variational approach, bypassing the Newtonian approach entirely, making this book stand out from its competitors
Applies a unique approach to teaching mechanics to advanced undergraduates with Lagrangian and Hamiltonian method that is far superior to that of Newton
Contains numerous exercises with concise solutions in the text and very detailed solutions in the manual

This is a textbook in the classical fashion with examples and ample homework problems. The material is arranged so that two or three different university courses at different academic levels can be based upon it. This text can be used as a basis for continuing education short courses or independent self study.

Authors: Nolting, Wolfgang
Targets deeper understanding of Hamilton and Lagrangian mechanics, giving a sturdy base for understanding quantum mechanics in later semesters
Offers a tried-and-tested approach reflecting the author's 40 years of teaching experience
Belongs to a multi-volume introduction to theoretical physics, in which one renowned textbook author covers the complete curriculum
Offers detailed explanations of the solutions to numerous problems