(adsbygoogle = window.adsbygoogle || []).push({}); Please suggest a good book on Mechanics covering the following topics-

Newtonian Mechanics – difficulties to handle coupled equations, Constraints (both time dependent and time independent), Degrees of freedom, Generalised co-ordinates, Generalized force, potential and kinetic energy, Lagrange’s equation of motion and Lagrangian, Ignorable co-ordinates, Hamilton’s equation and Hamiltonian.

Also suggest books on Field theory and Vibration & Waves.The syllabus is as follows-

Module 2: Field Theory

2.1 Basic concepts of Vector, Scalar and Vector products, Areal vector, Concepts of field (Scalar and Vector fields, examples), Scalar and Vector point functions related to the field, Derivative of vector, directional Derivative of vector point function, Gradient of scalar field, Line integral, Potential energy and force.

5L

2.2 Vector field, Velocity field and flux, Divergence of vector field, Electrostatic field, its potential and flux, Divergence of electrostatic field, Gauss’ Law of Electrostatics, Gauss’s divergence theorem (No proof), Laplace’s equation, Poisson’s equation, (Application to Cartesian, Spherically and Cylindrically symmetric systems), Continuity equation.

5L

2.3 Curl of a vector field, Stoke’s theorem (No proof), Potential field, Curl of velocity field, Curl of magnetic field and Ampere’s Circuital law, its application in simple cases, Curl of electric field and divergence of magnetic field and the concepts of scalar and vector potentials.

5L

2.4 Faraday’s law of electro-magnetic induction, Maxwell’s field equations, Concept of displacement current, Maxwell’s wave equation and its solution for free space.

Module 3: Vibration and waves

3.1 Simple harmonic motion - its expression and differential equation, Superposition of two linear SHMs (with same frequency), Lissajous’ figures.

Damped vibration – differential equation and its solution, Critical damping, Logarithmic decrement, Analogy with electric circuits.

Forced vibration – differential equation, Amplitude and Velocity resonance, Sharpness of resonance and Quality factor.

Progressive wave equation and its differential form, Difference between elastic (mechanical) and electromagnetic waves.

8L

3.2 General concept of Polarisation, Plane of vibration and plane of polarization, Malus’s law, Qualitative discussion on Plane, Circularly and Elliptically polarized light, Polarisation through reflection and Brewster’s law, Double refraction (birefringence) - Ordinary and Extra-ordinary rays, Polaroid, Nicol prism, Retardation plates and analysis of polarized lights.

6L

3.3 Huygen’s construction of wave surface and wave fronts, Interference of electromagnetic waves, Spatial and Temporal Coherence, Conditions for sustained interference, Conservation of energy and intensity distribution, Interference through division of wave front – Theory and application of Fresnel’s Bi-prism experiment, Interference through division of amplitude – Thin film interference, Fringes of equal thickness and equal inclination, Theory and application of Newton’s ring experiment.

8L

3.4 Diffraction of light – Fresnel and Fraunhofer class, Theory of Fraunhofer diffraction for single slit and double slits, Intensity distribution, Extension to N-slits and plane transmission grating, Missing orders and Resolving power of grating.

Thanking you all.

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# Homework Help: Good book on Mechanics

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