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Course Undergraduate
Semester Sem. IV
Subject Code PH222
Subject Title Classical Mechanics

Syllabus

Brief survey of the Newtonian mechanics of a particle and systems of particles; Constraints , generalised coordinates, D'Alembert's principle and Lagrange's equation, velocity dependent potential and dissipation function.
Variational principles and Lagrange's equations, Lagrange multipliers, conservation theorems and symmetry properties; Central force motion, Kepler's laws ,
orbital dynamics , stability of circular orbits , precession of equinoxes and of satellite orbits ;
Rigid body motion, Euler angles, inertia tensor and moment of inertia.
Euler's equations of motion, free motion of rigid bodies, motion of symmetric top.
Hamiltonian's canonical equations of motion, Routh's procedure; Principle of least action; Small oscillations, normal coordinates and normal mode frequencies.
Canonical transformations, equations of canonical transformations, symplectic approach.
Poisson Brackets (PB) and canonical invariants , infinitesimal canonical transformations , Noether's theorem conservation laws in the PB formulation , angular momentum PB relations
Hamiltonian-Jacobi theory of linear oscillatory systems, Hamiltonian's principal and characteristic functions, separation of variables, action-angle variables;
Hamilton-Jacobi theory, geometrical optics and wave mechanics.
Dynamical systems: First order autonomous systems, basic theory and examples, Area preserving transformations, Transformations with dilation, Second order autonomous systems, fixed points equilibrium and stability, separation of variables, classification and determination of fixed points, limit cycles.

Text Books

1.    Goldstein, H - Classical Mechanics, Addison Wesley, 2nd ed., 1980.
2.    Biswas, S. N - Classical Mechanics, Books and Allied, 1998. 

References

1.    Rana, N. C and P. S. Jog - Classical Mechanics, Tata McGraw Hill, 1991.
2.    Arnold,V. I - Mathematical Methods of Classical Mechanics, Springer Verlag, 1981.  
3.    Hand, L. N and J. D. Finch - Analytical Mechanics, Cambridge University Press, 1998.
4.    L. Breklhovskikh, L and V. Gancharov - Mechanics of Continua and Wave dynamics, Springer Verlag, 1985.
5.    Lai, W. M  D. Rubin and E. Krempl - Introduction to Continuum Mechanics, Pergamon Press, 1978.
6.    Sommerfeld, A - Mechanics Academic Press, 1952.
7.    Percival, I and S. Richards - Introduction to Dynamics Cambridge University Press, 1982.
8.    Landau, L. D and E. M. Lifshitz - Mechanics, Pergamon Press, 1960.