Classical Mechanics-I A course given at University of Hyderabad Summer Semester May14 - July10 (2018) |

### Part-I From Newton to Euler and Lagrange

- Review of Newtonian Mechanics
- Euler Lagrange Equations
- Energy Conservation, Cyclic Coordinates

### Part-II Action Principle

- Hamilton's Principle
- Noether's Theorem
- Examples

### Part-III Hamiltonian Form of Dynamics

- Hamiltonian Equations of Motion
- Poisson Brackets, EOM in Poisson Bracket Form
- Variational Principle in Phase Space

### Part-IV Spherically Symmetric Potentials

- General Properties of Motion
- Solving Equations of Motion
- Keplar problem, bounded orbits
- Unbounded orbits

### Part-V Scattering

- BasicDefinitions
- Scattering of Waves
- Why callit cross setion?
- Computing cross section
- Lab and center of mass frames

### Part-VI Small Oscillations

- Oscillations in One Dimension
- A Simple Example in Two Dimensions
- Normal Frequencies and Norma lModes of Vibration
- Several Degreesof Freedom
- Examples

### Part-VII Galilean Transoformations, Noninertial Frames,

- Galiliean Transformations
- Accelerated Linear Motion
- Rotation Group
- Motion in a Rotating Frame;
- Centrifugal and Coriolis Forces

### Part-IX Canonical Transformations

- Variatonal Principle in Phase Space
- Canonical Transformations;
- Properties of Canonical Transfomations
- Infinitesimal Canonical Transformations

### Part-X Hamilton Jacobi Theory

- Hamilton's Principal Function
- Jacobi's Complete Integral
- Time Independent Hamilton Jacobi Equation
- Solution of Separation of Variables
- Examples

### Assignment, Quiz, Test and Examination Papers

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