Classical Mechanics e-bog

Classical mechanics is one of those special occurrences in science where interdisciplinary contributions have come together in a perfect blend, providing a most elegant and penetrating example of "e;modeling"e; in science. Following Lagrangrian principles, the author employs mathematics not only as a "e;unifying"e; language, but also to exemplify its role as a catalyst behind new concepts and discoveries, such as the d'Alembert principle, complex systems dynamics, and Hamiltonian mechanics. Today, these same dynamics are now being focused to address other interdisciplinary areas of research in fields such as biology and chemistry.Key topics and features:* Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles* Analytical mechanics, such as Lagrange's equations, are explicitly derived, placing them on sound mathematical and physical ground* Attention to the topic of "e;small oscillations and stability"e;, intended to serve as groundwork to the atomic theory of vibrations of atoms in molecules* Hamilton-Jacobi mechanics is treated with an eye to recent developments in the solvability of Hamilton-Jacobi PDEsOffering a rigorous mathematical treatment of the subject and requiring of the reader only a solid background in introductory physics, multivariable calculus, and linear algebra, Classical Mechanics can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists.