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Techniques of classical mechanics : from Lagrangian to Newtonian mechanics

Author: Samya Zain; Institute of Physics (Great Britain),
Publisher: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2019]
Series: IOP expanding physics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Samya Zain's work fulfills the niche that connects introductory physics level books, like Physics 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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Samya Zain; Institute of Physics (Great Britain),
ISBN: 9780750320764 0750320761 9780750320757 0750320753
OCLC Number: 1084752471
Notes: "Version: 20190101"--Title page verso.
Description: 1 online resource (various pagings) : illustrations (some color).
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.
Series Title: IOP expanding physics.
Responsibility: Samya Zain.

Abstract:

Samya Zain's work fulfills the niche that connects introductory physics level books, like Physics 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.

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