# Variational Principles in Classical Mechanics

## Dublin Core

### Subject

### Description

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.

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.

### Creator

Douglas Cline

### Publisher

University of Rochester River Campus Libraries

### Contributor

Cut Rita Zahara

### Rights

Creative Commons

### Type

### Files

### Collection

### Citation

Douglas Cline, “Variational Principles in Classical Mechanics,”

*Open Educational Resource (OER)*, accessed January 23, 2022, http://oer.iain-padangsidimpuan.ac.id/items/show/304.