Mechanics

by Chaichian, Masud; Merches, Ioan; Tureanu, Anca

• ISBN13: 9783642163906
• ISBN10: 3642163904
• Format: Hardcover
• Copyright: 2012-01-04
• Publisher: Springer Verlag

Summary

This book on Classical Mechanics is addressed to advanced seniors and beginning graduate students who have physics as a major discipline, it offers a general view on analytical formalism and shows how it can be applied in different branches of theoretical physics, like thermodynamics, statistical physics, electrodynamics, field theory, magnetofluid dynamics, special theory of relativity and non-linear dynamics.Why a new book on Classical Mechanics? First, because Classical Mechanics has undergone an important revival during the last 10-15 years, associated with the progress in non-linear dynamics, applications of Noether's theorem in both discrete and continuous systems, and last, but not least, the extension of variational principles in different boundary sciences (Magnetofluid Dynamics, etc.). Second, because there is need for a book mainly concerned with the applied analytical formalism, which was first developed within the frame of Classical Mechanics, and then proved to be a very useful tool of investigation in different physical disciplines.The first chapter is concerned with the basic notions, principles and fundamental theorems of Newtonian mechanics for one- and many-particle systems, performing the necessary connection between the undergraduate courses on mechanics and analytical methods. The second chapter obtains the Lagrangian approach using differential (D'Alambert) and variational (Hamiltonian) principles. Special attention is given to Noether's theorem and its applications in mechanics of discrete systems. The third chapter deals with important applications of the Lagrangian formalism, such as central and elastic force fields and gravitational pendulum. A separate paragraph deals with the classical collision between particles. In Chapter IV the Lagrangian approach is applied to the study of a rigid body. The chapter concludes with several special applications and electromagnetic analogies. In the fifth chapter one passes from the Lagrangian to the Hamiltonian approach, the derivation of canonical equations is followed by several applications in mechanics and electrodynamics. The final chapter treats the analytical formalism applied in mechanics of continuous deformable media, this enables the study of elastic medium and ideal fluids. Applications in electrodynamics and magnetofluid dynamics are given.Mathematical appendices and over 130 problems with solutions complete this new type of textbook on Classical Mechanics.