## Description

**Candidates can get Best Physics Galaxy Mechanics Board**** ****Books 2018 also a Top List of Main Study Materials for 2017-2018 entrance exam in India.**

**Physics Galaxy Mechanics – Vol. 1**by GKP

**Syllabus****:**

**1. Complex Variable and Functions:** Function of complex variable, Cauchy‟s theorem, Cauchy‟s integral formula, contour integration, branch points, branch cuts, singular points, Taylor and Laurent expansion, Schwartz reflection principle, residue theorem for evaluation of definite integrals, analytic continuation, Gamma function.

**2. Complex Mapping:** Transformation or mapping, Complex mapping functions, some general transformations, translation, rotation, stretching, inversion, the liner transformation, Conformal mapping.

**3. Second Order Linear Differential equations with variable coefficients:** Power series solution method; Legendre polynomial, Hermite polynomial, Bessel‟s polynomial, Lagurre polynomial, Hypergeometric and Confluent Hypergeometric functions; Green‟s function method.

**Objective:** This course has been so framed that the students are first exposed to the mathematical tools needed in Mechanics and Special Relativity. Students are then taught the topics of conservation laws, elastic and inelastic scattering, dynamics of rigid bodies and inverse-square law of forces in the framework of Newtonian Mechanics.

**Fundamentals of dynamics:** Motion of Charged particles in electric and magnetic fields.Dynamics of a system of particles. Centre of mass. Conservation of momentary. Idea of conservation of momentum from Newton’s third law. impulse. Momentum of variable mass system: motion of rocket, work-energy theorem. Potential energy. Energy diagram. Stable and unstable equilibrium. Conservative and non-conservative forces. Force as gradient of potential energy. Particle collisions. Centre of mass frame and laboratory frame

**Conservation Laws:** Conservation of Energy, Conservative forces, Internal forces and conservation of linear momentum, Centre of mass, systems with variable mass, Space-Vehicle Problem. Conservation of Angular Momentum, Internal torques, Angular Momentum about the Centre of mass, Rotational invariance, Shape of Galaxy. (Chs. V and VI of Book 2, Ch. 5 of Book 3).

**Elastic and Inelastic Scattering :** Types of scattering and conservation laws, Laboratory and centre of mass systems, collision of particles which stick together, General elastic collision of particles of different mass, Cross-section of elastic scattering, Rutherford scattering. (Ch. VI of Book 1, Ch. 7 of Book 2).

**Dynamics of Rigid Bodies :** Equation of motion, angular momentum and kinetic energy of a Rotating Body, Moment of Inertia and Radius of Gyration, Rotation of about fixed axes – time dependence of motion, cylinder on an accelerated rough plane, Behaviour of angular momentum vector, Principal axes and Euler’s equations. Elementary Gyroscope, Symmetrical Top. (Ch.VIII of Book 2, Ch. 8 of Book 3).

**Inverse-Square-Law of Forces :** Force between a Point Mass and Spherical shell. Force between a Point Mass and Solid Sphere, Gravitational and Electrostatic self-energy. Gravitational energy of the Galaxy and of uniform sphere; Orbits and their eccentricity, Two-body problem – reduced mass. (Ch. IX of Book 2, Ch. 6 of Book 3).

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