Following Lagrangrian principles, this book employs mathematics not only as a unifying language, but also to exemplify its role as a catalyst in such new concepts and discoveries as the d'Alembert principle, complex systems dynamics, and Hamiltonian mechanics.

Classical mechanics is one of those special intersections in science where interdisciplinary contributions come together to provide an elegant and penetrating example of "modeling". Following Lagrangrian principles, the author employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst for new concepts and discoveries, such as the d'Alembert principle, complex systems dynamics, and Hamiltonian mechanics. Today, these same dynamics are being focused to address other interdisciplinary areas of research in fields such as biology and chemistry. Offering 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.

Offers a rigorous mathematical treatment of mechanics as a text or reference Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries Includes supplementary material: sn.pub/extras

Klappentext
Classical mechanics is a chief example of the scientific method organizing a "complex" collection of information into theoretically rigorous, unifying principles; in this sense, mechanics represents one of the highest forms of mathematical modeling. This textbook covers standard topics of a mechanics course, namely, the mechanics of rigid bodies, Lagrangian and Hamiltonian formalism, stability and small oscillations, an introduction to celestial mechanics, and Hamilton–Jacobi theory, but at the same time features unique examples—such as the spinning top including friction and gyroscopic compass—seldom appearing in this context. In addition, variational principles like Lagrangian and Hamiltonian dynamics are treated in great detail.

Using a pedagogical approach, the author covers many topics that are gradually developed and motivated by classical examples. Through `Problems and Complements' sections at the end of each chapter, the work presents various questions in an extended presentation that is extremely useful for an interdisciplinary audience trying to master the subject. Beautiful illustrations, unique examples, and useful remarks are key features throughout the text.

Classical Mechanics: Theory and Mathematical Modeling may serve as a textbook for advanced graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference or self-study guide for applied mathematicians and mathematical physicists. Prerequisites include a working knowledge of linear algebra, multivariate calculus, the basic theory of ordinary differential equations, and elementary physics.

Inhalt
Preface.- Geometry of Motion.- Constraints and Lagrangian Coordinates.- Dynamics of a Point Mass.- Geometry of Masses.- Systems Dynamics.- The Lagrange Equations.- Precessions.- Variational Principles.- Bibliography.- Index.