**by Douglas Cline**

DescriptionTable of ContentsDetailsHashtagsReport an issue ### 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. ### Table of Contents

### Book Details

### Related Books

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).

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

Title

Variational Principles in Classical Mechanics

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

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