Course

UNIT 1:Review of basic principles, Conservative systems, Conservation of linear momentum, Phase space-phase portrait – Dynamical Systems – Phase space dynamics – stability analysis.UNIT 2:Lagrangian and Hamiltonian Mechanics with Constraints-Euler-Lagrange Equations, DAlembert and Hamilton principles, Conservation Laws, holonomic and nonholonomic constraints Generalized co-ordinates -Calculus of Variation, Principle of least action – The Lagrangian, Lagranges Equations, Degrees of Freedom, Generalized momentum & Hamiltons Equations.UNIT 3:Central forces – Keplers laws – bound state and scattering states. Determining the Motion using Energy Integral- Laboratory frame and centre of mass frame- Scattering.UNIT 4:Rotational Dynamics of Rigid Bodies: Conservation of Angular momentum, Moment of Inertia, Rotational Kinetic Energy, Euler Angles, Inertia Tensor, The Euler Equations-Analysis of a symmetric Top-Gyroscopes.UNIT 5:Hamiltonian: Hamiltons equations using Legendre Transformation- Cyclic co-ordinates- Application of Hamiltons formalism in solving dynamical Problems.

Course ObjectivesThe objective of the course is intended to impart a basic knowledge on Central forces and Rotational dynamics.Course OutcomesAt the end of the course, students will be able toCO1: Understand the significance of conservative systems and Phase Space dynamics.CO2: Understand the concept of constraint, principle of least action and formulation of Lagranges method and apply Lagranges equation for simple dynamical systems.CO3: Understand Central force and its applications in Keplers, Scattering problems and Centre of mass problems.CO4:Understand the basics of rotating frames of references, Euler angles and Eulers equations.CO5: Apply Hamiltons equations in solving dynamical problems.

TEXT / REFERENCE BOOKS:1.Herbert Goldstein, John Safko Charles P. Poole, Classical Mechanics, Pearson, 3rd Ed, 2011.2.Landau, Lev D., and Evgenij M. Lifshitz. Mechanics: Course of Theoretical Physics. Vol.1.Butterworth-Heinemann; 3rd Ed, 1982. ISBN 978-0750628969.3.John Taylor, Classical Mechanics, University Science Books, 1st Ed, 2004.4.S. T. Thomton and J B Marion, Classical Dynamics of Particles and Systems, Brooks Cole, 1st Ed, 2009.5.Walter Greiner, Classical Mechanics: Point Particles and Relativity, Springer Verlag, 1st Ed, 2004.