## Course Detail

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

### Syllabus

##### 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.

 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

### 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 – https://www.youtube.com/
watch?v=Q6Gw08pwhws&list=PL5E4E56893588CBA8
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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