Variational Principles in Classical Mechanics

by Douglas Cline

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Book Description

Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering. This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.

This 2nd edition adds discussion of the use of variational principles applied to the following topics:
1) Systems subject to initial boundary conditions;
2) The hierarchy of the related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries;
3) Non-conservative systems;
4) Variable-mass systems;
5) The General Theory of Relativity.

This open book is licensed under a Creative Commons License (CC BY-NC-SA). You can download Variational Principles in Classical Mechanics ebook for free in PDF format (16.9 MB).

Table of Contents

Chapter 1
A brief history of classical mechanics
 
Chapter 2
Review of Newtonian mechanics
 
Chapter 3
Linear oscillators
 
Chapter 4
Nonlinear systems and chaos
 
Chapter 5
Calculus of variations
 
Chapter 6
Lagrangian dynamics
 
Chapter 7
Symmetries, Invariance and the Hamiltonian
 
Chapter 8
Hamiltonian mechanics
 
Chapter 9
Hamilton's Action Principle
 
Chapter 10
Nonconservative systems
 
Chapter 11
Conservative two-body central forces
 
Chapter 12
Non-inertial reference frames
 
Chapter 13
Rigid-body rotation
 
Chapter 14
Coupled linear oscillators
 
Chapter 15
Advanced Hamiltonian mechanics
 
Chapter 16
Analytical formulations for continuous systems
 
Chapter 17
Relativistic mechanics
 
Chapter 18
The transition to quantum physics
 
Chapter 19
Epilogue
 

Book Details

Publisher
River Campus Libraries
Published
2019
Pages
589
Edition
2
Language
English
ISBN13
9780998837291
ISBN10
0998837296
ISBN13 Digital
9780998837284
ISBN10 Digital
0998837288
PDF Size
16.9 MB
License
CC BY-NC-SA

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