Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Lagrangian formulation of mechanics. Degrees of freedom and equations
of motion. Constraints and Generalized coordinates. Principle of least
action. Emphasis on the Variational principle. The Calculus of
Variations. Euler-Lagrange equations. Constrained systems and Lagrange
multipliers.
- Phase space formulation. Hamiltonian, phase space, Poisson brackets.
Canonical transformations. Liouville's theorem and Poincare
recurrence. Hamilton-Jacobi theory. Action-angle variables.
- Oscillators. Small fluctuations. Damped,forced and anharmonic.
Eigenvalue equation and principle axis transformation, normal
coordinates, forced oscillations and resonance, vibrations of
molecules. Nonlinear oscillations and chaos.
- Motion in a central field. Equivalent one-body problem. first
integrals, classification of orbits, virial theorem, Bertrand's
theorem Kepler's law. Symmetries and conservations laws. Noether's
theorem. Central forces in three dimensions. Scattering in a
central force field, Rutherford scattering.
- Rigid bodies. Rotation. Orthogonal transformations, Euler angles,
rigid body dynamics, spinning top.
- H. Goldstein, C. P. Poole and J. L. Safko, Classical mechanics,
03rd edition, Addison-Wesley (2001).
- L. D. Landau and E. M. Lifshitz, Mechanics, 03rd edition,
Butterworth Heinemann (1976).
- N. C. Rana and P. S. Joag, Classical Mechanics, Tata McGrawHill
(1992).
- V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, Mathematical
aspects of classical and celestial mechanics, 03rd edition, Springer
(2006).
- J. V. Jose and E. J. Saletan, Classical dynamics: a contemporary
approach, Cambridge University Press (1998).
- W. Greiner, Classical Mechanics - Systems of Particles and
Hamiltonian Dynamics, Springer (2002).
