Foucault pendulum

Geometric Mechanics — 1st Semester 2020/2021

Lecturer: José Natário
Office: Mathematics Building, 4th floor, room 4.29
Classes: Wednesdays and Fridays from 9:00 to 11:00 in classrooms E1 and Q5.1
Office Hours:  Wednesdays from 16:00 to 18:00 in this Zoom session


The final grades are now available (see side bar).

You can find more information about the tennis racket theorem in this video.

You can see a dramatic implementation of the Lagrange top this video.

You can see surprising motions of mechanical systems with nonholonomic constraints here, here and here. See an explanation of the first video in this paper (or solve exercise 4.15.(11) in the book).

To understand the origin of the designation "completely integrable system" solve question 3 in this exam.

You can find more information about the KAM Theorem here.

You can learn more about cosmology on this webpage.


Geometric Mechanics: mechanical systems, holonomic constraints, rigid body, non-holonomic constraints, Lagrangian mechanics, Hamiltonian mechanics, completely integrable systems, symplectic and Poisson geometry, symmetry and reduction.

Relativity: Galileo spacetime, special relativity, Cartan connection, general relativity, Schwarzschild solution, cosmology.




Grading Policy

Homework: There will be weekly problem sets making up 50% of the grade. Late homework will not be accepted.

Final exam: There will be a final exam counting 50% towards the grade. Students will be able to repeat this exam if necessary.


For more exercises check the course webpages from previous years (mostly in Portuguese):

Final exams

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