## Details of PH3101 (Autumn 2018)

Level: 3 |
Type: Theory |
Credits: 4.0 |

Course Code | Course Name | Instructor(s) |
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PH3101 |
Intermediate Classical Mechanics |
Chiranjib Mitra |

Preamble |
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This is an intermediate course on Classical Mechanics. This is a core course for 3rd year BS-MS and 1st year IPhD students. |

Syllabus |
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Free and constrained systems. Classification of constraints. Actual
and virtual displacements. Ideal constraints. Principle of virtual work and DAlemberts principle. Generalized coordinates. Generalized forces. Lagranges equation for Potential forces. Applications to simple systems. Conservation laws. The Jacobi function and the Hamiltonian. Legendre transformations. Hamiltons canonical equations. Poisson brackets. The cotangent bundle. Canonical transformations. Liouvilles theorem. The variational principle and Lagranges equations. Rigid body dynamics. Euler angles. The Euler equations of motion. Torque free rigid body motion. The heavy symmetric top. Small oscillations. Normal modes and coordinates. Scattering by central forces. The differential cross section for Rutherford scattering. Dynamics of simple non-linear systems. Stability of autonomous and non-autonomous systems. Equilibrium, limit cycle, quasi-periodicity and chaos. |

Prerequisite |
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Basics of physics. |

References |
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1. L.. D. Landau and E. M. Lifschitz, Course on theoretical physics
Vol. 1 : Mechanics, Butterworth-Heinemann, London (1998). 2. F. Gantmacher, Lectures in Analytical Mechanics, translated by G. Yankovsky, Mir Publishers, Moscow (1975). 3. H. Goldstein, C. Poole and J. Safko, Classical Mechanics, Pearson (2002). 4. J. V. Jose and E.J. Saletan, Classical dynamics - a contemporary approach, Cambridge University Press, Cambridge (1998). 5. V.I. Arnold, Mathematical methods of classical mechanics, translated by K. Vogtmann and A. Weinstein, Springer, Berlin (1981). 6. Steven H. Strogatz, Nonlinear Dynamics And Chaos, Perseus Books Group, (1994) |

#### Course Credit Options

Sl. No. | Programme | Semester No | Course Choice |
---|---|---|---|

1 | IP | 1 | Core |

2 | IP | 3 | Not Allowed |

3 | IP | 5 | Not Allowed |

4 | MR | 1 | Elective |

5 | MR | 3 | Not Allowed |

6 | MS | 5 | Core |

7 | RS | 1 | Elective |

8 | RS | 2 | Elective |