Instructor: Stefano Profumo

Office: ISB, Room 325

Phone Number: 831-459-3039

Office Hours: Wednesday 2PM - 3:30PM, or by appointment

E-mail: profumo AT scipp.ucsc.edu

Click here to download the syllabus in PDF format

Lecture Times: Mondays, 3:15PM - 5:10PM (incl. 10' break); Wednesdays 3:00PM - 4:55PM (incl. 10' break)

Lecture Location: ISB 231

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 Chaos

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

*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

Lect. | ~ Date | Topic | Reading (Goldstein+P+S) |
---|---|---|---|

1 | 9/26 | Preliminary remarks; Lagrangian formalism | 1.1-1.4 |

2 | 9/28 | Lagrangian methods: examples; Hamilton's principle | 1.5-1.6; 2.1 |

3 | 10/3 | Calculus of variations; Hamilton's principle with constraints | 2.2-2.5 |

4 | 10/5 | Symmetries and conservation laws | 2.6-2.7 |

5 | 10/10 | Central force problem; Closed orbits; Virial theorem | 3.1-3.7 |

6 | 10/12 | Scattering in a central force field | 3.10-3.11 |

7 | 10/17 | Lenz vector; Three-body problem; Numerical methods | 3.9; 3.12 |

8 | 10/19 | Coordinate transformations; Euler angles | 4.1-4.5 |

9 | 10/24 | Infinitesimal and finite rotations; Coriolis effect | 4.6-4.10 |

10 | 10/31 | Inertia tensor; Rigid-body motion | 5.1-5.6 |

11 | 11/2 | Small oscillations and related examples | 6.1-6.4 |

12 | 11/7 | Legendre transformation and Hamilton equations of motion | 8.1-8.2; 8.4 |

13 | 11/9 | Principle of least action; Canonical transformations | 8.5-8.6; 9.1-9.2 |

14 | 11/14 | Canonical transformations: examples; Poisson brackets | 9.3-9.7 |

15 | 11/16 | Symmetry groups; Liouville's theorem; Hamilton-Jacobi theory | 9.8-9.9; 10.1-10.2 |

16 | 11/21 | Hamilton Jacobi theory and applications | 10.3-10.6 |

17 | 11/23 | Classical chaos; Attractors | 11.1-11.3 |

18 | 11/28 | Poincare' maps | 11.4-11.5 |

19 | 11/30 | Bifurcations; Logistic equation; Fractals | 11.6-11.9 |

- HW#1: handed out on 10/10, due on 10/17
- HW#2: handed out on 10/24, due on 10/31
- HW#3: handed out on 11/14, due on 11/21
- HW#4: handed out on 11/30, due on 12/8

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

HW Set #1 | phys210_HW01.pdf | Monday 10/17 |

HW Set #1 - sol. to #2 | HW1_sol2.pdf | |

HW Set #2 | phys210_HW02.pdf | Monday 10/31 |

HW Set #3 | phys210_HW03.pdf | Monday 11/21 |

HW Set #3 - sol. to #1 | HW3_sol1.pdf | |

HW Set #3 - sol. to #3 | HW3_sol3.pdf | |

HW Set #4 | phys210_HW04.pdf | Thursday 12/8 |

Final Solutions | phys210_final_solutions.pdf | Thursday 12/8 |

- Lorenz Attractor
- Rossler Attractor
- Youtube video of Henon-Heiles map
- Forced Pendulum (1)
- Forced Pendulum (2)
- Double Pendulum
- Time series of logistic map
- Bifurcation diagram of logistic map
- Mandelbrot Set

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.