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Mechanics



ISBN 9780849309793
Published November 13, 2000 by Narosa
190 Pages

 
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Book Description

Based on a course developed by the author, Mechanics provides an introduction to classical mechanics. Each chapter begins with an introduction to the topics under discussion and is followed by precise definitions, propositions, and theorems and ends with exercises that reinforce students understanding. The treatment of the subject is mathematical, but the mathematics used is elementary. In fact, all the mathematics presented involve basic vector algebra and differential calculus of vector valued functions of a real variable. The author avoids explaining the underlying geometry in an explicit manner. Instead, he presents geometric discussions in a kinematical disguise - a treatment beneficial not only to the mathematics student but also to students of physics and engineering.

Table of Contents

Preface
BASIC CONCEPTS OF MOTION
Introduction
Concepts of a Particle
Motion of a Particle
Motion of a Plane
Polar Coordinates
Equation of Motion

RECTILINEAR MOTION
Introduction
Equation of Rectilinear Motion
Integration of Equation of Motion
Some Qualitative Analysis

FIRST INTEGRALS OF MOTION
Introduction
Conservative Force Fields
Energy, Momentum and Torque
Conservation Principles
Use of Conservation Principles

CENTRAL FORCE FIELDS
Introduction
Basic Properties
Equation of Motion in Polar Coordinates
Integration of Equations of Motion
An Explanation
Circular Orbits
Force Field from Equation of Orbit
Planetary Motion (Kebler's Problem)

SYSTEM OF PARTICLES
Introduction
A System of Particles
The Center of Mass
Some More Definitions
Conservation Principles
The Two Body Problem
Some Solved Examples

RIGID DYNAMICS
Introduction
The Nature of Motion
The Instantaneous Angular Velocity
Equations of Motion
The Inertia Tensor
Euler's Equations
Symmetric Rigid Bodies

LAGRANGIAN MECHANICS
Introduction
Generalized Coordinates
Motion
The Lagrangian Function
Lagrange's Equations
Hamilton's Principle of Least Action
Hamilton's Equations of Motion
Conservation Principles

Supplementary Reading
Index

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