Syllabus

Survey of Newtonian mechanics & forces of constraints, homogeneity and isotropy of space and time: conservation laws. Lagrangian and Hamiltonian Mechanics: Generalized co-ordinates, configuration and phase space, cyclic co-ordinates and conservation theorem, variational principle, principle of least action, derivation of Lagrange's equation, extension of Hamilton's principle to systems with constraints, Legendre transformation and Hamilton's equations, Roth's procedures. Central force problem: reduction of two body problem to one body problem, Virial theorem, integrable power law potentials, Bertrand's theorem, inverse square law, Laplace-Runge-Len vector, scattering in central force.

To gain deeper understanding and solving problems of classical mechanics by using Lagrangian and Hamiltonian approach.

CO1: Recognizing the shortcoming of Newtonian approach in finding the equation of motion involving constraint forces and addressing
the same via Lagrangian approach.
CO2: To learn the use of variational principle in mechanics.
CO3: Utility of Lagrangian method to mechanical and non-mechanical systems.
CO4: Learning the Hamilton's method of solving equation of motion.
CO5: To gain an understanding of topics such as central forces and solving problems related to it.

H. Goldstein, Classical Mechanics, Addison Wesley, Pearson Education, 2007.

S. T. Thornton & J. B. Marion, Classical Dynamics, Cengage Learning, 5th Ed. 2008.

L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics- Mechanics, (vol.-1), 3rd Ed., Pergamon Press.

R. D. Gregory, Classical Mechanics, Cambridge University Press, 2006.