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CLASSICAL MECHANICS
- The student will be able to apply knowledge to calculate the Calculus of variation and its application to simple problems, formulation of Lagrangian and Hamiltonian for a problem, Canonical transformation and Action angle variable.
- The student shall acquire ability to differentiate between problems of classical and quantum nature and apply classical methods to solve the relevant problems.
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Course |
Learning outcome (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Paper Code |
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PHY 121 |
Classical Mechanics |
After completion of the course the student will be able to
CO 1: Understand the basic concepts of coordinate systems and degrees of freedom and will be able to apply the same in various problems.
CO 2: Learn about Hamilton's and Lagrange's Equations using calculus of variation and apply them to solve problems of mechanics.
CO 3: Gain Knowledge of Conservation principles, Noether's theorem, Eulerian angles and Euler’s theorem and will be able to apply these concepts to relevant problems.
CO 4: Understand Canonical transformation and Lagrange's and Poisson’s brackets and be able to analyze their relations.
CO 5: Learn about the Action angle variables and their applications |
Approach in teaching: Interactive Lectures, Discussion, problem solving in Tutorials, Demonstration.
Learning activities for the students: Self learning assignments, Effective questions, Simulation, Seminar presentation, Solving numerical.
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Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations |
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.
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.
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.
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.
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.
- “Classical Mechanics”, Goldstein, Addison Wesley
- “Mechanics-Volume I “, Landau. And Lifshiz,
- “Classical Mechanics “, A. Ray choudhary.
- “Classical Mechanics” N.C. Rana and P.S. Joag, Tata Mc Graw Hill
- “Classical Mechanics” J.C. Upadhyaya, Himalaya Publishing House.
