Variational Principles in Classical Mechanics
The goal of this book is to introduce the reader to the intellectual beauty, and philosophical implications,of the fact that nature obeys variational principles that underlie the Lagrangian and Hamiltonian analyticalformulations of classical mechanics. These variational methods, which were developed...
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| Summary: | The goal of this book is to introduce the reader to the intellectual beauty, and philosophical implications,of the fact that nature obeys variational principles that underlie the Lagrangian and Hamiltonian analyticalformulations of classical mechanics. These variational methods, which were developed for classical mechanicsduring the 18 th ? 19 th century, have become the preeminent formalisms for classical dynamics, as well as for many other branches of modern science and engineering. The ambitious goal of this book is to lead the student from the intuitive Newtonian vectorial formulation, to introduction of the more abstract variational principles that underlie the Lagrangian and Hamiltonian analytical formulations. This culminates in discussion of thecontributions of variational principles to the development of relativistic and quantum mechanics. The broadscope of this book attempts to unify the undergraduate physics curriculum by bridging the chasm thatdivides the Newtonian vector-di?erential formulation and the integral variational formulation of classicalmechanics, and the corresponding chasm that exists between classical and quantum mechanics. Powerfulvariational techniques in mathematics, that underlie much of modern physics, are introduced and problemsolving skills are developed in order to challenge students at the crucial stage when they ?rst encounter thissophisticated and challenging material. The underlying fundamental concepts of classical mechanics, andtheir applications to modern physics, are emphasized throughout the course. |
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| Item Description: | http://oer.library.unej.ac.id//index.php?p=show_detail&id=599 532 |