Techniques of classical mechanics : from Lagrangian to Newtonian mechanics / Samya Zain.

Format:

Book

Author/Creator:

Zain, Samya, author.

Contributor:

Institute of Physics (Great Britain), publisher.

Series:

IOP (Series). Release 6.

IOP expanding physics

[IOP release 6]

IOP expanding physics, 2053-2563

Language:

English

Subjects (All):

Mechanics.

Physical Description:

1 online resource (various pagings) : illustrations (some color).

Place of Publication:

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2019]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

text file

Biography/History:

Samya Zain gained her PhD at The State University of New York at Albany and was awarded the Best Teaching Assistant Award for the year 2002. She is currently Associate Professor of Physics and Department Head of Physics at Susquehanna University and was awarded the distinguished teaching award there in 2016. She has been a member of the BABAR scientific research collaboration at SLAC (Stanford Linear Accelerator Center), at Stanford University, California and the ATLAS collaboration at CERN.

Summary:

Samya Zain's work fulfils the niche that connects introductory physics level books, like Phyiscs by Halliday, Resnick and Krane, to graduate level books like Analytical Mechanics by Fowles and Cassiday and The Variational Principles of Mechanics by Cornelius Lanczos. The book has been class-tested on Samya's own students on her Newtonian Mechanics course at Susquehanna University, and is accompanied by her own website, which features problems and exercises that will be regularly updated to match students' needs. This book serves as an excellent stepping stone from level 1 introductory physics to graduate level physics and provides a level field for the various techniques used to solve problems in classical mechanics, and to explain more simply the Lagrangian and Hamiltonian methods, and it is a must for junior and senior physics undergraduates.

Contents:

1. Foundations

1.1. The nature of science

1.2. Units

1.3. International system of units (SI)

1.4. Dimensional analysis

1.5. A quick review of vectors

1.6. Derivatives of vectors

1.7. Position vector

1.8. Transformation between various coordinate systems

1.9. Velocity and acceleration

1.10. Velocity and acceleration in various coordinates

2. Conservation laws

2.1. Introduction

2.2. Conservation laws

2.3. Forces that depend on position : energy considerations

2.4. One-dimensional conservative system : complete solution

3. Newtonian mechanics

3.1. Introduction

3.2. Rectilinear motion under uniform acceleration

3.3. Linear momentum

3.4. Newton's laws of motion

3.5. Torque

4. Lagrangian mechanics

4.1. Lagrangian mechanics

4.2. From Newtonian to Lagrangian formalism

4.3. Choosing Lagrange's formalism

when and where?

4.4. Lagrangian formalism for non-conservative forces

4.5. The Lagrangian formalism in a nutshell

5. Hamiltonian mechanics

5.1. Hamiltonian mechanics

5.2. The Hamiltonian principle

5.3. Classical and quantum mechanics

6. Waves and oscillations

6.1. Mechanical waves

6.2. Physical properties of waves

6.3. Standing waves

6.4. Resonance

7. Simple harmonic oscillation

7.1. Harmonic oscillator

7.2. Energy consideration in harmonic oscillator

7.3. About various pendulums

7.4. Simple gravity pendulum

7.5. Elastic pendulum

7.5..1 Elastic pendulum

Lagrangian mechanics

7.6. Spherical pendulum

8. Gravitation and central forces

8.1. Introduction

8.2. Newton's law of universal gravitation

8.3. Gravity

8.4. Gravitational force between a uniform sphere and a particle

8.5. Potential energy in a gravitational field : gravitational potential

8.6. Kepler's law of planetary motion

9. Two- and three-dimensional dynamics

9.1. Introduction : general principles

9.2. Some useful mathematical concepts

9.3. Conservative and non-conservative forces in 3D

9.4. Generalized conservation of energy principle in 3D

9.5. The energy equation

9.6. Body with variable mass

10. Circular and projectile motion

10.1. Motion in higher dimensions

10.2. Uniform circular motion

10.3. Rotational motion

10.4. Rectilinear motion and rotation about a fixed axis

10.5. Harmonic oscillator in higher dimensions

10.6. Motion of a projectile in a uniform gravitational field

10.7. Projectile motion : no air resistance

11. Fluid-statics

11.1. Types of materials

11.2. Fluid-statics

11.3. Pressure and density in fluid-statistics

11.4. Pressure in fluid-statistics

11.5. Archimedes' principle

11.6. Specific gravity

11.7. Pascal's principle

11.8. Center of buoyancy

12. Fluid resistance

12.1. Fluid resistance

12.2. Forces as a function of velocity : fluid resistance

12.3. A falling object under linear drag

12.4. Falling object : the quadratic case

12.5. Projectile motion : air resistance

12.6. Damped harmonic oscillator in 1D

13. Fluid dynamics

13.1. Fluid dynamics

13.2. Fluid flow

13.3. Viscosity

13.4. Bernoulli's principle

13.5. Velocity of the fall of a sphere through a viscous liquid

13.6. Turbulent motion and Reynolds number

14. Properties of solids

14.1. Solids

14.2. Stress

14.3. Strain

14.4. Waves in solids

15. Rotation

motion of rigid bodies

15.1. Rigid bodies

15.2. Moment of inertia

15.3. Mass on an incline

15.4. Laminar motion of a rigid body

16. System of particles

16.1. System of particles

16.2. Two-particle system

16.3. Many-particle systems

16.4. Conservation of momentum in a system of

16.5. Collisions

16.6. 1D collision in the center-of-momentum reference frame

17. Scattering theory

17.1. Cross-section

17.2. Types of scattering

17.3. Neutral cross-section

17.4. Capture cross-section

17.5. Repulsive cross-section

17.6. Scattering of alpha particles

Appendices. A. Unit conversion

B. Velocity and acceleration in various coordinates

C. Noether's theorem

D. Configuration space.

Notes:

"Version: 20190101"--Title page verso.

Includes bibliographical references.

Title from PDF title page (viewed on February 4, 2019).

Other Format:

Print version:

ISBN:

9780750320764

9780750320757

Access Restriction:

Restricted for use by site license.