Constraints - Generalized coordinates, Holonomic and non-holonomic systems, Scleronomic and Rheonomic systems. D’Alembert’s principle and Lagrange’s equations – Velocity – dependent potentials and the dissipation function – some applications of the Lagrange formulation.

Hamilton’s principle – Some techniques of calculus of variations – Derivation of Lagrange’s Equations from Hamilton’s principle – Extension of Hamilton’s principle to non-holonomic systems – Conservation theorems and symmetry properties.

Legendre Transformations and the Hamilton Equations of motion-canonical equations of Hamilton – Cyclic coordinates and conservation theorems – Routh’s procedure - Derivation of Hamilton’s equations from a variational principle – The principle of least action.

The equations of canonical transformation – Examples of Canonical transformations – Poisson Brackets and other Canonical invariants. The simplistic approach to canonical transformations.

Hamilton Jacobi equations for Hamilton’s principle function – Harmonic oscillator problem - Hamilton Jacobi equation for Hamilton’s characteristic function – Separation of variables in the Hamilton-Jacobi equation – Action angle variables in systems of one degree of freedom.