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MATH 277A Geometric Mechanics
TTh 12:30pm-1:50pm, APM 5829.
- Prof. Melvin Leok
Office: APM 5763
Office Hours: TBA, or by appointment.
- Course Handout
- The resources below are password protected with the user name ma277a,
and the password is the first 4 digits of:
- As there is no TA for this class, there will be no assessed homework.
- However, Prof. Darryl Holm, the author of one of the supplementary
references, has a good
collection of homework problems, and solutions:
- You are encouraged to look over these problems, and try to work out
some of these for yourself. If you would like suggestions for which ones
to concentrate on, please contact Prof. Leok.
- This course will introduce geometric mechanics at the graduate level, which involves the use of geometric and symmetry techniques in the analysis of mechanical systems. In particular, we will discuss the variational principles and geometric structures that underly the Lagrangian and Hamiltonian formulation of mechanics, as well as introducing the relevant tools of differential geometry, such as manifolds, exterior calculus, and Lie groups. The course will culminate in a discussion of how symmetry and reduction theory serve as a unified basis for understanding the Eulerian description of rigid body dynamics and fluid mechanics.
- Some exposure to analytical mechanics is helpful, but not essential.
The course will introduce the relevant differential geometric tools as
well as the relevant aspects of analytical mechanics.
You should consider these additional references as a potential source of advanced topics in geometric mechanics, which would be suitable for further study, as part of your course project.
- Taeyoung Lee, Melvin Leok, Harris McClamroch, Global Formulations of Lagrangian and
Hamiltonian Dynamics on Manifolds, Springer-Verlag, 2018. [ Electronic Version ]
- Darryl Holm, Geometric
Mechanics - Part I: Dynamics and Symmetry, Second Edition,
Imperial College Press, 2011. ISBN: 184816775X. [ Electronic Version ]
- Ralph Abraham, Jerrold Marsden, Foundations
of Mechanics, Second Edition, American Mathematical Society 2008.
ISBN: 0821844385. [ Electronic Version ]
- Ralph Abraham, Jerrold Marsden, Tudor Ratiu, Manifolds,
Tensor Analysis, and Applications, Second Edition, Springer-Verlag
1988. ISBN: 0387967907. [ Draft of Third Edition ]
- Vladimir Arnold, Mathematical
Methods of Classical Mechanics, Second Edition, Springer-Verlag 1989. ISBN: 0387968903.
[ Electronic Version ]
- Anthony Bloch, Nonholonomic
Mechanics and Control, Springer-Verlag, 2010. ISBN: 1441930434.
[ Electronic Version ]
- Theodore Frankel, The
Geometry of Physics, Second
Edition, Cambridge University Press, 2003. ISBN: 0521539277. [ Electronic Version ]
Mechanics - Part II: Rotating, Translating and Rolling, Second
Edition, Imperial College Press, 2011. ISBN: 1848167784. [ First Edition ]
- Darryl Holm, Tanya Schmah, Cristina Stoica, Geometric
Mechanics and Symmetry, Oxford University Press, 2009. ISBN:
0199212910. [ Electronic Version ]
- Chris Isham, Modern
Differential Geometry for
Physicists, Second Edition, World Scientific, 1999. ISBN:
9810235623. [ Electronic Version ]
- Jerrold Marsden, Lectures
on Mechanics, Cambridge
University Press, 1992. ISBN: 0521428440. [ Draft of Second Edition ]
- Your grade in the course is based on your project and your 20-minute
project presentation during the time of the final.
- The topic of your project should be decided in consultation with the
instructor before the end of the first month of class.