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CLASSICAL MECHANICS
Paper Code:
PHY121
Credits:
04
Contact Hours:
60.00
Max. Marks:
100.00
12.00
Unit I:
UNIT I
Basic concepts of coordinate systems and degrees of freedom; Holonomic and non-holonomic constraints; D-Alembert's Principle; Generalized coordinates; Principle of virtual work; Lagrangian, Lagrange's equation and its applications; Velocity dependent potential in Lagrangian formulation; Generalized momentum; Hamilton's Principle; Lagrange’s equation from Hamilton's Principle.
12.00
Unit II:
UNIT II
Calculus of variation and its application to simple problems: Hamilton's Equations; Applications of Hamilton’s equation; Hamilton’s canonical equation in different coordinate systems; Calculus of Variation and Euler-Lagrange’s equations; Brachistochrone Problem; Derivation of Lagrange's and Hamilton’s canonical equation from Hamilton’s variational principle; Method of Lagrange's undetermined multipliers; Principle of least action.
12.00
Unit III:
UNIT III
Conservation principle and Noether's theorem; Conservation of energy, linear momentum and angular momentum as a consequence of homogeneity of time and space and isotropy of space respectively.
Eulerian angles; Euler’s theorem; Angular momentum and Inertia Tensor; Euler’s equations; Euler’s equation of motion for a rigid body.
12.00
Unit IV:
UNIT IV
Canonical transformation: Legendre transformations; Generating functions; Conditions for Canonical transformation; Bilinear invariant conditions; Lagrange's and Poisson’s brackets and their relations; Angular momentum and Poisson Brackets; equation of motion in Poisson bracket formulation; Invariance of Poisson’s and Lagrange’s Brackets under canonical transformations; Liouville's theorem.
12.00
Unit V:
UNIT V
Action angle variable: Hamilton Jacobi equation and its applications; adiabatic invariance of action variable; The Kepler problem in action angle variables; theory of small oscillations in Lagrangian formulation; theory of small oscillations in normal coordinates and normal modes; Two coupled oscillator and solution of its differential equation; Two coupled pendulum; Double pendulum.
References:
1. “Classical Mechanics”, Goldstein, Addison Wesley
2. “Mechanics-Volume I “, Landau. And Lifshiz,
3. “Classical Mechanics “, A. Ray choudhary.
4. “Classical Mechanics” N.C. Rana and P.S. Joag, Tata Mc Graw Hill
5. “Classical Mechanics” J.C. Upadhyaya, Himalaya Publishing House.
Academic Year:
