Variational Principles in Classical Mechanics
| Main Author: | Douglas Cline |
|---|---|
| Other Authors: | Cut Rita Zahara |
| Format: | Book eBook |
| Terbitan: |
University of Rochester River Campus Libraries
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| Subjects: | |
| Online Access: |
http://uilis.unsyiah.ac.id/oer/items/show/304 http://uilis.unsyiah.ac.id/oer/files/original/d05bf42fe839cfd25094019429c9a639.pdf |
Daftar Isi:
- 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 analytical formulations of classical mechanics. These variational methods, which were developed for classical mechanics during 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 the contributions of variational principles to the development of relativistic and quantum mechanics. The broad scope of this book attempts to unify the undergraduate physics curriculum by bridging the chasm that divides the Newtonian vector-differential formulation and the integral variational formulation of classical mechanics, and the corresponding chasm that exists between classical and quantum mechanics. Powerful variational techniques in mathematics, that underlie much of modern physics, are introduced and problem solving skills are developed in order to challenge students at the crucial stage when they first encounter this sophisticated and challenging material. The underlying fundamental concepts of classical mechanics, and their applications to modern physics, are emphasized throughout the course.