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Geometric Mechanics — 1st Semester 2015/2016




Lecturer: José Natário
Email: jnatar@math.ist.utl.pt
Office: Mathematics Building, 4th floor, room 4.29
Classes: Tuesdays and Thursdays from 14:30 to 16:30.
Office Hours:  Wednesdays from 14:00 to 16:00.



Announcements

The final grades are available (see side bar). If you want to take a look at your graded exams come to my office at your convenience.

You can see surprising motions of mechanical systems with nonholonomic constraints here.

You can see the motion of a Lagrange top here.

You can see examples of the instability of free rigid body rotations about the intermediate axis here.

You can see the two normal modes of the double pendulum near its stable equilibrium point here.




Syllabus

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.




Bibliography

Main

Secondary




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. You will be able to repeat this exam if necessary.




Homework

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




Final exams



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