Course Details
Subject {L-T-P / C} : PH2004 : Introduction To Classical Mechanics { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Pawan Kumar
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.
Course Objectives
- To gain deeper understanding and solving problems of classical mechanics by using Lagrangian and Hamiltonian approach.
Course Outcomes
CO1: Recognizing the shortcoming of Newtonian approach in finding the equation of motion involving constraint forces and addressing the same via Lagrangian approach. <br />CO2: To learn the use of variational principle in mechanics. <br />CO3: Utility of Lagrangian method to mechanical and non-mechanical systems. <br />CO4: Learning the Hamilton's method of solving equation of motion. <br />CO5: To gain an understanding of topics such as central forces and solving problems related to it.
Essential Reading
- H. Goldstein, Classical Mechanics, Addison Wesley, Pearson Education, 2007.
- S. T. Thornton & J. B. Marion, Classical Dynamics, Cengage Learning, 5th Ed. 2008.
Supplementary Reading
- 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.