| Course Name | Classical Mechanics II |
| Course Code | 22PHY502 |
| Semester | 7 |
| Credits | 4 |
Learning objectives
Understand the motivation for transformation
Study the technique of canonical transformation
To write down generating function for a given canonical transformation
Canonical Transformations: Equations of Canonical transformation, Examples-Simple Harmonic Oscillator, Liouville’s Theorem. Volume preservation in phase Space, Generating function, Conditions for canonical transformation and problem.
Learning objectives
Definition and properties of Poisson brackets
Application of Poisson bracklets
Poisson Brackets: Definition, Identities, Poisson theorem, Jacobi-Poisson theorem, Jacobi identity, invariance of PB under canonical transformation- Angular momentum Poisson bracket- Symmetry, invariance and Noether’s theorem.
Learning objectives
Hamilton- Jacobi Equation –its formation
Application of HJ equation
Action- Angle Variable
Hamilton- Jacobi Theorem: Hamilton- Jacobi Equation for Hamilton’s principal function, Hamilton- Jacobi Equation for Hamilton’s Characteristic Function, Harmonic oscillator problem, Action –angle variable in Systems of one variable, Kepler Problem in Action-angle variable.
Learning objectives
Theory of small oscillations- Eigen value problems
Apply the theory to various applications
Small oscillations: Formal theory of small oscillations as Eigen value problems, applications to diatomic and triatomic molecules, modes of vibrations.
Learning objectives
Introduction to Chaos
Elements of Non-linear dynamics- simple examples
Introduction to Chaos and Nonlinear Dynamics: Fixed points, Bifurcation, and Limit cycles, Lorenz Equations, The Logistic Map, Fractals and Strange Attractors.
Pre-requisites: – Mechanics, Classical Mechanics 1, Mathematics 1&2
Course Objectives: To study, understand and apply principles of Hamiltonian dynamics to solve dynamical systems
Course outcomes
CO1: Study canonical transformations and apply it to mechanical problems
CO2: Study the properties of Poisson’s bracket and apply it to dynamical problems
CO3: Apply Hamilton Jacobi theory for Harmonic oscillator and Kepler problem
CO4: Apply small oscillation theory developed in getting the frequencies of different of modes of oscillations in a coupled system
CO5: Introduction to Chaos and Nonlinear dynamics
Skill: Analytical skill to formulate dynamical problem and solve using Lagrangian Formalism.
| POs | PO1 | PO2 | PO3 | PO4 | PO5 | PSO1 | PSO2 | PSO3 |
| CO1 | 3 | 3 | 3 | 3 | ||||
| CO2 | 3 | 3 | 3 | 3 | ||||
| CO3 | 3 | 3 | 3 | 3 | ||||
| CO4 | 3 | 3 | 3 | 3 | ||||
| CO5 | 3 | 3 | 3 | 3 |
CO-PO Mapping
| Assessment | Internal | External Semester |
| Periodical 1 (P1) | 15 | |
| Periodical 2 (P2) | 15 | |
| *Continuous Assessment (CA) | 20 | |
| End Semester | 50 |
*CA – Can be Quizzes, Assignments, Projects, and Reports.
Justification for CO-PO Mapping
| Mapping | Justification | Affinity level |
| CO1-CO 5 to PO2 and PSO 1 | This is course with objective of building basic analytical skills to formulate problems and solve using techniques developed. There for it has highest affinity towards PO2 and PSO 1 | 3 |
| CO1-CO5-PO3 and PSO2 | This course develops problem solving skills and form a core course in Physics which will help student to formulate research problems – hence has strong affinity towards PO3 and PSO 2 | 3 |
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