Syllabus

Unit-I	Constraints and their classification, principle of virtual work, de’Almbert’s principle, various forms of Lagrange’s equations of motion for holonomic systems, examples.
Unit-II	Euler-Lagrange equations in various forms (statements only), Hamilton’s variational principle, derivation of Lagrange’s equation from Hamilton’s variational principle, generalized momentum, cyclic coordinates, general conservation theorem, conservation of linear momentum and angular momentum in Lagrangian formalism and symmetry properties, energy function and conservation of total energy in Lagrangian formalism.
Unit-III	Hamilton’s canonical equation of motion, relation with Lagrange’s equation, cyclic coordinate, Routhian procedure, variational principle approach to Hamilton’s equation of motion, examples.
Unit-IV	Canonical transformations, generating functions, symplectic condition, infintesimal canonical transformations, examples. Poisson bracket, Lagrange bracket, formal solution of equations of motion in terms of Poisson brackets, examples.

Goldstein H., Poole C. and Safko J., Classical Mechanics, (Third Edition), Pearson Education, Inc., Indian Low Price Edition, 2002.
Bhatia V. B., Classical Mechanics, Narosa Publishing House, 1997.
Sankara Rao K., Classical Mechanics, Prentice-Hall of India, 2005.

Lecture Notes

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