# Classical Mechanics

## 1st Edition

**Authors:**A. Douglas Davis

**eBook ISBN:**9780323149402

**Imprint:**Academic Press

**Published Date:**1st January 1986

**Page Count:**464

## Description

Classical Mechanics focuses on the use of calculus to solve problems in classical mechanics. Topics covered include motion in one dimension and three dimensions; the harmonic oscillator; vector algebra and vector calculus; and systems of particles. Coordinate systems and central forces are also discussed, along with rigid bodies and Lagrangian mechanics.

Comprised of 13 chapters, this book begins with a crash course (or brief refresher) in the BASIC computer language and its immediate application to solving the harmonic oscillator. The discussion then turns to kinematics and dynamics in one dimension; three-dimensional harmonic oscillators; moving and rotating coordinate systems; and central forces in relation to potential energy and angular momentum. Subsequent chapters deal with systems of particles and rigid bodies as well as statics, Lagrangian mechanics, and fluid mechanics. The last chapter is devoted to the theory of special relativity and addresses concepts such as spacetime coordinates, simultaneity, Lorentz transformations, and the Doppler effect.

This monograph is written to help students learn to use calculus effectively to solve problems in classical mechanics.

## Table of Contents

Preface

1 Conversational Basic

1.1 Getting Started

1.2 Elegant Output

1.3 Sometimes More is Really Less

1.4 Into the Wild Blue

2 One-Dimensional Motion

2.1 Kinematics in One Dimension

2.2 Dynamics in One Dimension

2.3 Constant Force

2.4 Force as a Function of Time

2.5 Force as a Function of Position

2.6 Force as a Function of Velocity

3 The Harmonic Oscillator

3.1 Introduction

3.2 Simple Harmonic Oscillator

3.3 Power Series Representation of an Arbitrary Function

3.4 Damped Harmonic Oscillator

3.5 Forced Harmonic Oscillator

3.6 Application to AC Circuits

3.7 Simple Pendulum

3.8 Physical Pendulum

4 Vectors

4.1 Introduction

4.2 Vector Algebra

4.3 Vector Multiplication

4.4 Coordinate Systems

4.5 Vector Calculus

4.6 Vector Differential Operators

5 Motion in Three Dimensions

5.1 Introduction

5.2 Separable Forces

5.3 Three-Dimensional Harmonic Oscillator

5.4 Potential Energy Function

5.5 Motion in Electromagnetic Fields

6 Coordinate Systems

6.1 Introduction

6.2 Plane Polar Coordinates

6.3 Cylindrical Polar Coordinates

6.4 Spherical Polar Coordinates

6.5 Moving Coordinate Systems

6.6 Rotating Coordinate Systems

6.7 Motion Observed on the Rotating Earth

6.8 Foucault Pendulum

7 Central Forces

7.1 Introduction

7.2 Potential Energy and Central Forces

7.3 Angular Momentum and Central Forces

7.4 Inverse-Square Force

7.5 Kepler's Laws

7.6 Orbital Transfers and "Gravitational Boosts"

7.7 Radial Oscillations about a Circular Orbit

7.8 Gravity

7.9 Rutherford Scattering

8 Systems of Particles

8.1 N Particles, the General Case

8.2 Momentum

8.3 Motion with a Variable Mass—Rockets

8.4 Motion with a Variable Mass—Conveyor Belts

8.5 Collisions

8.6 Center of Mass Frame

9 Rigid Bodies

9.1 Center of Mass

9.2 Angular Momentum

9.3 Rotation about an Axis

9.4 Moment of Inertia Theorems

9.5 The Inertia Tensor

9.6 Principal Axes

9.7 Kinetic Energy

9.8 Euler's Equations

10 Lagrangian Mechanics

10.1 Introduction

10.2 Generalized Coordinates

10.3 Generalized Forces

10.4 Lagrange's Equations

10.5 Elementary Examples

10.6 Systems with Constraints

10.7 Applications

10.8 Ignorable Coordinates

10.9 Lagrangian Mechanics and a Rotating Top

10.10 Hamilton's Equations

10.11 Hamilton's Principle

11 Statics

11.1 Introduction

11.2 Plane Trusses

11.3 Method of Joints

11.4 Method of Sections

11.5 Cables under Distributed Loads

11.6 Parabolic Cables

11.7 Catenary Cables

11.8 Cables with Concentrated Loads

12 Fluid Mechanics

12.1 Introduction

12.2 Hydrostatics: Fluids at Rest

12.3 Moving with the Flow

12.4 Hydrodynamics

13 Special Relativity

13.1 Introduction

13.2 Galilean Relativity

13.3 Historical Background

13.4 Einsteinean Relativity/Spacetime Coordinates

13.5 Simultaneity

13.6 Lorentz Transformations

13.7 Application of the Lorentz Transformations

13.8 Minkowski Diagrams

13.9 Velocity Transformation

13.10 Doppler Effect

13.11 Momentum and Mass-Energy

13.12 Relativistic Mass

Appendices

A Conversational Pascal

B Calculus Review

C Multiple Integrals

D Matrix Multiplication

Index

## Details

- No. of pages:
- 464

- Language:
- English

- Copyright:
- © Academic Press 1986

- Published:
- 1st January 1986

- Imprint:
- Academic Press

- eBook ISBN:
- 9780323149402