Classical Mechanics

Abstract

Classical mechanics is a chief example of the scientific method organizinga "complex" collection of information into theoretically rigorous,unifying principles; in this sense, mechanics represents one of thehighest forms of mathematical modeling. This textbook covers standardtopics 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 spinningtop including friction and gyroscopic compass--seldom appearing inthis context. In addition, variational principles like Lagrangianand Hamiltonian dynamics are treated in great detail.Using a pedagogical approach, the author covers many topics that aregradually developed and motivated by classical examples. Through`Problems and Complements' sections at the end of each chapter, thework presents various questions in an extended presentation thatis extremely useful for an interdisciplinary audience trying to masterthe subject. Beautiful illustrations, unique examples, and usefulremarks are key features throughout the text.Classical Mechanics: Theory and Mathematical Modeling may serve asa textbook for advanced graduate students in mathematics, physics,engineering, and the natural sciences, as well as an excellent referenceor self-study guide for applied mathematicians and mathematical physicists.Prerequisites include a working knowledge of linear algebra, multivariatecalculus, the basic theory of ordinary differential equations, andelementary physics.