Geometric Mechanics — 1st Semester 2022/2023

Announcements

The final grades are now 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, here and here.

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

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

Homework: Makes up 50% of the grade. Late homework will not be accepted.

Final exam: Makes up 50% of the grade. Can be retaken if necessary.

Homework

• Homework 1 (due on October 13)
• Homework 2 (due on November 24)
• Homework 3 (due on January 5)
• Homework 4 (due on January 24)

Exams

• Exam 1
• Exam 2

You can see more exams on the course webpages from previous years (some in Portuguese):

• 2020/2021
• 2019/2020
• 2018/2019
• 2016/2017
• 2015/2016
• 2012/2013
• 2010/2011
• 2002/2003
• 2001/2002
• 2000/2001