Coming soon
Classical Mechanics
This course will enable the students:
- 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.
- To differentiate between problems of classical and quantum nature and apply classical methods to solve the relevant problems.
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Course Code |
Course Title |
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24DPHY701 |
Classical Mechanics (Theory)
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CO122: Solve the basic concepts of coordinate systems and degrees of freedom and apply on various problems. CO123: Develop Hamilton's and Lagrange's Equations using calculus of variation and apply them to solve problems of mechanics. CO124: Determine the Conservation principles, Noether's theorem, Eulerian angles and Euler’s theorem and apply to solve these concepts to relevant problems. CO125: Justify and create Lagrange's Poisson’s brackets and anonical transformation then analyze their relations. CO126: Solve the Action angle variables, Lagrangian formulation and their applications. CO127: Contribute effectively in Course specific interaction. |
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 |
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.
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.
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.Levels of biological diversity: genetic, species and ecosystem diversity
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.
· “Classical Mechanics” J.C. Upadhyaya, Himalaya Publishing House.
Suggested Readings:
· “Mechanics-VolumeI”, Landau.AndLifshiz.
· “ClassicalMechanics”,A.Raychoudhary.
· “Classical Mechanics” N.C. Rana and P.S. Joag, Tata Mc Graw Hill
E-content:
· https://www.cgaspirants.com/2019/09/download-classical-mechanics-by-dr-j....
