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

- Author:
- Zain, Samya
- Published:
- Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2019]
- Physical Description:
- 1 online resource (various pagings) : illustrations (some color).
- Additional Creators:
- Institute of Physics (Great Britain)

##### Access Online

- Series:
- 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, and Appendices. A. Unit conversion -- B. Velocity and acceleration in various coordinates -- C. Noether's theorem -- D. Configuration space.
- 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.
- Subject(s):
- ISBN:
- 9780750320764 ebook

9780750320757 mobi

9780750320740 print - Audience Notes:
- Junior and senior physics undergraduates.
- Note:
- "Version: 20190101"--Title page verso.
- Bibliography Note:
- Includes bibliographical references.
- Other Forms:
- Also available in print.
- Technical Details:
- Mode of access: World Wide Web.

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

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