Instructor: Stefano Profumo

Office: ISB, Room 325

Phone Number: 831-459-3039

Office Hours: Thursday 12:30PM - 1:30PM, or by appointment

E-mail: profumo AT ucsc.edu

Click here to download the syllabus in PDF format

Lecture Times: Wednesdays and Fridays, 3:20 PM - 4:55 PM

Lecture Location: ISB 235

The following classes are canceled: ** W Sept 28, F Sep 30, F Oct 14, F Nov 18, F Dec 2**. Lectures are rescheduled for **M Oct 3, M Oct 10, M Oct 17, M Oct 24, M Nov 21**, ISB 235, 9:45
-11:20 AM.

Emphasis will be given in particular to those principles and mathematical constructions relevant to modern physics (including quantum mechanics and general relativity), as well as to more classical physical applications.

A list of topics that will be covered in this course includes:

- Variational Principles
- Lagrangian Formulation
- Applications: the Central Force Problem, the Motion of Rigid Bodies, Small Oscillations
- Hamiltonian Formulation
- Canonical Transformations
- Hamilton-Jacobi Theory and Action-Angle Variables
- Classical Field Theory

*Classical Mechanics, 3rd edition*by Goldstein, Poole, and Safko

*Classical Field Theory*by D.E. Soper (highly recommended for Classical Field Theory part)*Classical Dynamics: a contemporary approach*by J.V. Jose' and E.J. Saletan (recommended)*Analytical Mechanics for Relativity and Quantum Mechanics*by O.D. Johns (recommended)*Mathematical Methods of Classical Mechanics*by Arnold*Analytical Mechanics*by Fasano and Marmi*The Elements of Mechanics*by Gallavotti*Theoretical Mechanics*by Neal Moore*Classical Mechanics*by Barger and Olsson*Mechanics*by Landau and Lifshitz*The Classical Theory of Fields*by Landau and Lifshitz

Lect. | Topic | Reading (Goldstein+P+S; *: Soper) |
---|---|---|

1 | Preliminary remarks; Lagrangian formalism | 1.1-1.4 |

2 | Lagrangian methods: examples; Hamilton's principle | 1.5-1.6; 2.1 |

3 | Calculus of variations; Hamilton's principle with constraints | 2.2-2.5 |

4 | Symmetries and conservation laws | 2.6-2.7 |

5 | Central force problem; Closed orbits; Virial theorem | 3.1-3.7 |

6 | Scattering in a central force field | 3.10-3.11 |

7 | Lenz vector; Three-body problem; Numerical methods | 3.9; 3.12 |

8 | Coordinate transformations; Euler angles | 4.1-4.5 |

9 | Infinitesimal and finite rotations; Coriolis effect | 4.6-4.10 |

10 | Inertia tensor; Rigid-body motion | 5.1-5.6 |

11 | Small oscillations and related examples | 6.1-6.4 |

12 | Legendre transformation and Hamilton equations of motion | 8.1-8.2; 8.4 |

13 | Principle of least action; Canonical transformations | 8.5-8.6; 9.1-9.2 |

14 | Canonical transformations: examples; Poisson brackets | 9.3-9.7 |

15 | Symmetry groups; Liouville's theorem; Hamilton-Jacobi theory | 9.8-9.9; 10.1-10.2 |

16 | Hamilton Jacobi theory and applications | 10.3-10.6 |

17 | Fields and transformation laws; stationary action and fields | 1*, 2* |

18 | Classical field theory; the electromagnetic field | 3*, 8* |

19 | Further general properties of Field Theories | 9* |

19 | Course Review |

Homework Set number | (PDF) | Due Date | Solutions |
---|---|---|---|

HW Set #1 | phys210_HW01.pdf | Friday 10/14 | HW1_solutions.pdf |

HW Set #2 | phys210_HW02.pdf | Friday 10/28 | HW2 Solutions (by John Tamanas) |

Midterm | phys210_midterm.pdf | Wednesday 11/9 | Midterm Solutions |

HW Set #3 | phys210_HW03.pdf | Monday November 21 | phys210_HW3_sol.pdf and Hanwen's solutions |

HW Set #4 | phys210_HW04.pdf | Thursday December 8, 11AM, ISB 235 (final exam) | Hanwen's solutions |

Final | phys210_final.pdf | Thursday December 8 | Final Solutions |

A proof of Bertrand's Theorem

A proof of Chasles' theorem

An alternate proof of Chasles' theorem

Philosophy (Knowledge) is written in that great book which ever lies before our eyes (I call it the Universe), but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word; without knowledge of those, it's a useless wandering in a dark labyrinth.