Syllabus

Module 1: (8 hours)
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.

Module 2: (9 hours)
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.

Module 3: (9 hours)
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.

Module 4: (10 hours)
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.

Module 5: (3 hours)
Some examples and problems of Central force problems from textbooks.

Solving mechanics of system of particles via Lagrangian and Hamiltonian formulations.

Utilization of variational principle in mechanics.

Using Lagrangian method to solve mechanics of mechanical and non-mechanical systems.

Learning Hamilton’s method to derive equations of motion.

5. Utilization of the above methods to solve central force problems.

At the end of the course, students will be able to:
CO1: Recognizing the shortcoming of Newtonian approach in finding the equation of motion involving constraint forces and addressing the same via Lagrangian and Hamiltonian formulations.

CO2: Learn the use of variational principle in mechanics.

CO3: Apply the Lagrangian method to mechanical and non-mechanical systems.

CO4: Learn Hamilton's method of solving equations of motion.

CO5: Gain an understanding of topics such as central forces and solving related problems.

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

J. R. Taylor, Classical Mechanics, University Science Books (2020).

L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics- Mechanics, Pergamon Press. , (vol.-1), 3rd Edition (1976).

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