Aero 660 Nonlinear [Flight] Dynamics

"The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living" Henri Poincaré

Course Description

Dynamics is the subject that deals with systems whose states evolve over time. This course is mainly about the qualitative analysis of linear and nonlinear dynamical systems with strong emphasis on understanding their behavior with respect to parameter changes. We will discuss two main types of dynamical systems: differential equations and maps. While most linear problems can be solved in closed form, nonlinear systems require approximate solution methods and can generally be understood qualitatively. Over the course we will learn various techniques to deal with nonlinear systems, and we will explore the behavior they exhibit. Topics include bifurcations, fractals, strange attractors, and chaos.

Instructor

Tamás Kalmár-Nagy
(Please address me as Dr. T or Dr. Kalmár-Nagy or Prof. Kalmár-Nagy)

Contact Information:
609C HRBB
kalmarnagy@tamu.edu
http://aero.tamu.edu/people/kalmarnagy/

Office Hours:
Thursdays 4:00-5:00pm

Course Website:
http://aeweb.tamu.edu/aero660/

Course Objectives

1) To introduce methods of classical nonlinear dynamics to students through examples from science and engineering.
2) To provide an opportunity to improve student ability to survey the literature, conduct independent research and write a scientific paper.
3) To serve as a foundation for courses on "Perturbation Methods", "Nonlinear Controls", etc.
4) To introduce online and offline tools for conducting successful research.

I am committed to make this an engaging and fun class, while maintaining high academic standards. I will do my best to help you succeed in this course, but the ultimate responsibility to learn and practice the material is on you!

Text Books and Websites

[1] Strogatz, S. H., Nonlinear Dynamics and Chaos, With Applications to Physics, Biology, Chemistry, and Engineering, Addison-Wesley, 2004

Recommended:
[2] Moon, F. C., Chaotic and Fractal Dynamics, John Wiley & Sons, 1992
[3] Kuznetsov, Y. A., Elements of Applied Bifurcation Theory, Springer-Verlag, New York, 2004
[4] Ott, E., Chaos in Dynamical Systems, Cambridge University Press, 1993
[5] Scholarpedia: Encyclopedia of Dynamical Systems.

Projects

September 25: Choose Project topic - you must discuss this with me.
Submit a 2-page Project Proposal with preliminary literature review.

December 4: Project due. Powerpoint presentation to the class.

Expectations for the project are high - you are expected to show initiative in learning dynamical systems theory and you should be able to convey what you have learned in a cogent manner by writing a scientific report with proper reasoning and mathematical derivations. You are free to choose a topic from your personal area of interest or from my "pet projects" list. I will of course be available for advice and help in working through your chosen topic; it is your responsibility to utilize my help. You should begin your research as soon as you can to avoid the "mad dash" towards the end of the term (last minute work will generally result in a low-quality project).

When your presentation is ready, you might want to make a dry run (of the presentation, obviously) in front of your friends. Listen to their questions/criticism. You will be graded in part on the originality of the topic chosen, the ambitiousness of the topic, the quality of the presentation/written report and the level/rigor (not necessarily quantity) of mathematics used.
Previous projects included: Analysis of the Lattice Lotka-Volterra Model, Pseudospectral Methods and Transient Growth in Hydrodynamic Stability of Parallel Flows, Exploring Delayed Feedback in the van Der Pol Oscillator using Perturbation Methods, ABCT: A (rudimentary) Bifurcation and Continuation Tool, Hopf Bifurcations in a Nonlinear Dynamic Model for Chip Segmentation in Machining, Nonlinear Analysis of Aeroelastic Phenomena in a Rigid Two-Degree of Freedom Wing Model, Dynamical System Analysis of Magneto-Hydrodynamic Decaying Isotropic Turbulence, Delay-Coupled Oscillators, etc.

Homeworks

There will be roughly one homework assignment per week.
1)Homework problems will be posted regularly on the website. The submission format is ONE good-quality pdf file (not to exceed 3MB in size) of your scanned assignment emailed to me by 9am on the due date. It is your responsibility to submit your assignment on time. Anticipate technical problems with scanning, mail server, etc.
2)Homework must be complete with all steps shown. You may use computer software (Matlab, Mathematica, Maple et al.) but you must describe what you did and show relevant computer output.
3)Make sure your work is neat (it reflects on you). Your name must appear on the top right corner of the first page. Specify course title, hw number and problem numbers.
4)Your final answer must be easily identifiable (either boxed, highlighted, underlined, separate from other work, etc.) and must be dimensionally correct.

Homework Grades:
The problems in this class are usually open-ended. My grading philosophy is:
1)A scientist obtains a solution to a problem based on physical understanding of the problem and the solution is supported through careful analysis (including clearly stating assumptions),
2)A good scientist tries to have a "gut-feeling" for the solution, i.e. hu should know when the solution is obviously (or probably) wrong (because of math or other errors),
3) Partial credit may be received if the solution procedure is clear, logical, and satisfies the above.
4) You should be able to critically evaluate someone else’s work, as well as your own. If you are not critical of your own work, you will not be able to produce high quality work in science/engineering. Learning to assess one's own progress contributes to the goal of the Department and the College to prepare our students to be life-long learners.

Therefore, students will grade their own assignments1 (based on the solutions posted after the due date) and will email me their graded homework as ONE good-quality pdf file (not to exceed 5MB in size) of the scanned assignment with corrections and grading clearly shown by 9 AM one week after the due date. In the self-grading exercise you should use a 0-100 scale, where you also decide the weights for the various problems based on difficulty of the ACTUAL solution (and not the time/effort you spent on that particular problem). I will assign the grade for your assignment based on both your original and self-graded solutions.

Teaming:
You are STRONGLY encouraged to work ALONE on your homework assignments and project. If you discuss a problem with someone else (that includes me), you MUST unambiguously show the name(s) of the other person(s) you received/given help from/to. I may, at my discretion, choose to quiz any class member on current or past assignments. If it becomes obvious that the person being quizzed does not adequately understand what they have affixed their signature to, this will be treated as an Honor Code violation. (See also Academic Integrity).

Grading Policy

Standard TAMU grading system.
A>=90%, 80%<=B<=89%, 70%<=C<=79%, 60%<=D<=69%, F<=59%.

10 HW at 5 pts each
50 pts

Project
50 pts

Total points
100 pts

Notes

Attendance:
I strongly recommend you to attend all classes and BE ON TIME (being consistently late is a sign of disrespect). If you need to miss a class, I would appreciate if you sent me an email explaining the reason, so that I am aware of any problems early on.

BEHAVIOR IN CLASS:
No laptops, cell phones, texting, iPod-ing, crossword puzzles. SU-DON’T-KU!
Please do not sleep in class. If you are so tired that you can’t keep your eyes open, please stay home and rest (propping eyes open with toothpicks has proven to be unhealthy). Your sleeping is disrespectful to the class.
Please help to keep our classrooms clean, even if you did not create the mess.

Academic Integrity:
"An Aggie does not lie, cheat or steal, or tolerate those who do."
Students should strive to uphold the Honor Code (http://www.tamu.edu/aggiehonor), to accept responsibility for learning, and to follow the philosophy and rules of the Honor System. There is no tolerance for cheating in any form. Remember, if you cheat the system, you cheat yourself, as well.

Accommodation for Students with Disabilities: The Americans with Disabilities Act is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe that you have a disability requiring accommodation, please contact the Department of Student Life, Services for Students with Disabilities, Cain Hall (979-845-1637, http://studentlife.tamu.edu/ssd). Any student needing accommodation due to disability, either in the classroom or during exams should let the instructor know privately during the first week of the semester.

Accommodation for Religious Observance: Texas HB256 (9/1/03): "An institution of higher education shall excuse a student from attending classes or other required activities, including examinations, for the observance of a religious holy day, including travel for that purpose. A student whose absence is excused under this subsection may not be penalized for that absence and shall be allowed to take an examination or complete an assignment from which the student is excused."
An effort will be made to accommodate students’ needs for religious observance. Students should contact me during the first week of class in order to make arrangements.

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