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PAPER VI: MECHANICS

Unit I
: Survey of Elementary principles: 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.

Unit II
: Variation principles and Lagrange’s equations: 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.

Unit III
: Hamilton Equations of motion: 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.

Unit IV
: Canonical transformations: The equations of canonical transformation – Examples of Canonical transformations – Poission Brackets and other Canonical invariants The symplectic approach to canonical transformations– integral invariants of Poincare, Lagrange brackets.

Unit V
: Hamilton Jacobi Theory: 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 – Actionangle variables in systems of one degree of freedom.

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