Syllabus

Survey of elementary principles: Degrees of freedom, Generalized coordinates. mechanics of single and many particle systems, conservation laws, D'Alembert principle and Lagrange's equations, velocity dependent potentials and dissipation functions.
Variational principle and Lagrange's equations: Variational principle and Lagrange's equations: derivation of Lagrange's equation from Hamilton's principle, extension of Hamilton's principle to systems with constraints, conservation theorems and symmetry properties.
Hamilton's equation of motion: Legendre transformation and Hamilton's equations, cyclic coordinates and conservation theorem, Routh's procedures, Hamilton's equation from variational principle, principle of least action.
Central force problem: Reduction of two body problem to one body problem, equation of motion and classification of orbits. Virial theorem, integrable power law potentials, Bertrand's theorem, inverse square force law, Laplace-Runge-Lenz vector, scattering in central force field in center of mass frame and laboratory coordinates.

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.