Syllabus for MATH 649K Section 2

Geometric Control of Mechanical Systems

Spring Semester 2008 CRN: 89172

Academic Expectations

Prerequisites: students should be proficient in multi-variable differential calculus and multi-variable integral calculus. Students should also have some knowledge of linear and multi-linear algebra, particularly finite-dimensional inner-product spaces, and some knowledge of differential equations. Useful, but not mandatory, prerequisites include: a course in advanced calculus (inverse function theorem, implicit function theorem, ...), a course in curves and surfaces in Euclidean 3-space (Frenet frame, first and second fundamental forms, mean curvature, Gaussian curvature, ...), a course on manifolds and Riemannian geometry (coordinate charts, tangent bundle, cotangent bundle, vector fields, differential forms, Riemannian metric, covariant derivative, connection ...), some experience with Lie groups and Lie algebras, especially the special orthogonal group, SO(n). Most of these topics will be covered in class, but it certainly will not hurt if you have seen at least some of them before.

Students should review the Statement of Academic Expectations. All academic work should be done with the high levels of honesty, integrity and excellence that this University demands.

Readings

The plan is to cover Chapter 4 (Simple Mechanical Control Systems), some of Chapter 7 (Controllability) and some of Chapter 8 (Low-order controllability and kinematic reduction).

The textbook, which will not be available at the Campus Center Book Store, should be purchased from another source. The following files supplement the text book and should be downloaded.

• Notes for the class room lectures.
• Notes on Lagrangian Mechanics.
• Is it worth learning differential geometric methods?

Attendance and Grading

Regular attendance to class lectures is required. The grade will be determined by two in-class midterm exams, a cumulative final exam, and homework. Homework assignments and due dates will be posted on the MATH 649K Homework page. Homework assignments must be legible, and you are required to use proper grammatical English and follow the guidelines for clear and concise writing. The exams and homework will be weighted as follows:

You must bring your UH student ID to every test. If Keller Hall is closed for any reason, we will meet by the steps of Hamilton Library. Only documented valid health related excuses will be accepted for missing an exam.

Last modified: Sun Apr 6 11:08:23 HST 2008