Geometric Mechanics — 1st Semester 2012/2013

Announcements

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

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

• Godinho and Natário, An Introduction to Riemannian Geometry

Secondary

• Arnold, Mathematical Methods of Classical Mechanics
• Marsden and Ratiu, Introduction to Mechanics and Symmetry
• Oliva, Geometric Mechanics
• Schutz, A First Course in General Relativity

Grading Policy

Tests: There will be two tests each counting 35% towards the grade (dates to be arranged). You will be able to make up for one of these tests the week after classes end.

Homework: There will be weekly problem sets making up 30% of the grade. Late homework will not be accepted.

Homework

• Week 1 (due on September 28)
• Week 2 (due on October 9)
• Week 3 (due on October 12)
• Week 4 (due on October 19)
• Week 5 (due on October 26)
• Week 6 (due on November 2)
• Week 7 (due on November 9)
• Week 8 (due on November 16)
• Week 9 (due on November 23)
• Week 10 (due on November 30)
• Week 11 (due on December 7)
• Week 12 (due on December 14)
• Week 13 (due on December 21)

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

• 2010/2011
• 2002/2003
• 2001/2002
• 2000/2001

Tests

• Test 1
• Make up test 1/Test 2
• Make up test 1/Make up test 2