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Course Detail

Course Name Classical Mechanics II
Course Code 22PHY502
Semester 7
Credits 4


Unit 1

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.

Unit 2

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.

Unit 3

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.

Unit 4

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.

Unit 5

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.

Objectives & Outcomes

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.

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

Text Books

  1. H. Goldstein, C. Poole and J. Safko, Classical Mechanics, Pearson Education, 3rd Edition, 2011.
  2. Landau and Lifshitz, Mechanics, Butterworth-Heinemann, 3rd Edition, 1982.
  3. Walter Greiner, Classical Mechanics: Systems of Particle and Hamiltonian Dynamics, Springer,2nd Edition, 2009
  4. Lecture Series on Classical Physics by Prof. V. Balakrishnan –
  5. Steven H Strogatz, Non Linear Dynamics and Chaos, Perseus Books Publishing, 1994.

Evaluation Pattern

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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