Thursday, 20 November 2008

Aerospace Dynamics

Oleh:
Arip Nurahman
Department of Physics
Faculty of Sciences and Mathematics, Indonesia University of Education

and

Follower Open Course Ware at Massachusetts Institute of Technology
Cambridge, USA
Department of Physics
http://web.mit.edu/physics/
http://ocw.mit.edu/OcwWeb/Physics/index.htm
&
Aeronautics and Astronautics Engineering
http://web.mit.edu/aeroastro/www/
http://ocw.mit.edu/OcwWeb/Aeronautics-and-Astronautics/index.htm

Staff

Instructors:
Prof. Jonathan How
Prof. John Deyst

Course Meeting Times

Lectures:
Two sessions / week
1.5 hours / session

Level

Undergraduate

16.61 Aerospace Dynamics

Spring 2003

A gyroscope, adapted from Lecture 14. (Image courtesy of MIT OCW.)

Course Highlights

This course on Aerospace Dynamics includes a complete set of lecture notes and assignments, as well as an extensive reference reading list. Topics extend to analysis of both aircraft flight dynamics and spacecraft attitude dynamics, based upon presented principles and equations of motion.

Course Description

This undergraduate course builds upon the dynamics content of Unified Engineering, a sophomore course taught in the Department of Aeronautics and Astronautics at MIT. Vector kinematics are applied to translation and rotation of rigid bodies. Newtonian and Lagrangian methods are used to formulate and solve equations of motion. Additional numerical methods are presented for solving rigid body dynamics problems. Examples and problems describe applications to aircraft flight dynamics and spacecraft attitude dynamics.

Syllabus

Instructors

Prof. Jonathan P. How
Prof. John Deyst

Course Objectives

Review of the basic Newtonian dynamics
- Focus on 3D motion
- Gyroscopic and rotational dynamics
- Formal approaches for handling coordinate transformations
Lagrangian formulation of the equations of motion
Analysis of aircraft flight dynamics and stability
Analysis of spacecraft attitude dynamics

Administrative

Review of Newtonian dynamics ≈ 6 lectures
Lagrangian dynamics ≈ 6 lectures
Rigid body motions in 3D ≈ 6 lectures
Aircraft/spacecraft dynamics ≈ 6 lectures
- Midterm exam #1 in class (1 hour) after Lecture 6 (15%)
- Midterm exam #2 in class (1 hour) after Lecture 14 (20%)
- Final exam at the end of the semester (30%)
- Homework - Out Thursdays, due following Thursday at beginning of class (35%)
  Hand-in in class or drop-off at my office. Collaboration: You can discuss problems
  with others, but you are expected to write up and hand in your own work.
- You will definitely need access to MATLAB^®

Textbooks

None required. Lecture notes will be handed out in class. But various books available for reference are:

Meriam and Kraige. Engineering Mechanics - Dynamics. Wiley, 2001.
Hibbeler. Engineering Mechanics - Statics and Dynamics. Prentice Hall.
Beer and Johnston. Vector Mechanics for Engineers. McGraw-Hill.
Greenwood. Principles of Dynamics. 2nd ed. Prentice Hall [RB dynamics].
Williams, Jr. Fundamentals of Applied Dynamics. Wiley, 1996.
Baruh. Analytical Dynamics. McGraw Hill [fairly advanced].
Wells. Schaum's Outline of Lagrangian Dynamics. McGraw-Hill, 1967.
Goldstein. Classical Mechanics. 2nd ed. Addison Wesley [very advanced].

Learning Objectives for Students Graduating from 16.61 will be Able to:

Use methods of vector kinematics to analyze the translation and rotation of rigid bodies - and explain with appropriate visualizations.
Identify appropriate coordinate frames and calculate the transformations between them.
Formulate and solve for the equations of motion using both the Newtonian and Lagrangian formulations.
Use the basic equations of motion to calculate the fundamental flight modes of an aircraft.
Use the basic equations of motion to calculate the attitude motions of a low Earth orbit spacecraft.

Measurable Outcomes for Students Graduating from 16.61 will be Able to:

Derive the equations of motion in accelerating and rotating frames.
Solve for the equations of motion using both the Newtonian and Lagrangian formulations.
Simulate and predict complex dynamic behavior of vehicles such as projectiles, aircraft, and spacecraft.
Use MATLAB^® as a tool for matrix manipulations and dynamic simulation.
Linearize the 6DOF motions associated with most dynamic behavior to establish the basic modes of the motion.

MATLAB^® is a trademark of The MathWorks, Inc.

Exams

This course included three exams. The first two exams were administered during the semester, and the final took place during the week immediately following the end of classes. The first two exams, and the solution to the first, are included here.

Midterm Exam #1 (PDF)
Midterm Exam #1 Solutions (PDF)
Midterm Exam #2 (PDF)

Assignments

This section includes a complete set of assignments for the course. Problem sets were assigned approximately once every week, and were typically due one week later. Graded problem sets were returned to students after another week. Performance on problem sets comprised 35% of a student's final grade.

Assignment #1 (PDF)
Assignment #2 (PDF)
Assignment #3 (PDF)
Assignment #4 (PDF)
Assignment #5 (PDF)
Assignment #6 (PDF)
Assignment #7 (PDF)
Assignment #8 (PDF)
Assignment #9 (PDF)
Assignment #10 (PDF)

Calendar

This calendar incorporates the lecture schedule and the assignment schedule. Some lecture topics may have required more than one class session to cover.


LEC #	TOPICS	ASSIGNMENTS


1	Aerospace Dynamics


2	Coriolis "Demystified"	HW1 Issued


3	Dynamics


4	Introduction to Multiple Intermediate Frames	HW1 Due HW2 Issued


5	Momentum, Angular Momentum, and Dynamics of a System of Particles	HW2 Due HW3 Issued


6	Numerical Solution of Nonlinear Differential Equations	HW3 Due


	Midterm Exam #1


7	Lagrange's Equations


8	Examples Using Lagrange's Equations Handout: Examples (from Lagrangian and Hamiltonian Mechanics by M. G. Calkin. River Edge, NJ: World Scientific Publishing Co. Pte. Ltd., 1999.)	HW4 Issued


9	Virtual Work and the Derivation of Lagrange's Equations


	Virtual Work and the Derivation of Lagrange's Equations (Continued)	HW4 Due HW5 Issued


10	Friction in Lagrange's Equations


	Friction in Lagrange's Equations (Continued)	HW5 Due HW6 Issued


11	Kinematics of Rigid Bodies


12	Rigid Body Dynamics	HW6 Due HW7 Issued


13	Axisymmetric Rotations


14	Gyroscopes	HW7 Due HW8 Issued


	Gyroscopes (Continued)	HW8 Due


	Midterm Exam #2	HW9 Issued


15	Spacecraft Attitude Dynamics


	Spacecraft Attitude Dynamics (Continued)	HW9 Due HW10 Issued


16	Aircraft Dynamics


17	Aircraft Longitudinal Dynamics	HW10 Due


18	Aircraft Lateral Dynamics


	Final Exam

Lecture Notes

These lecture notes were made available to students in the class electronically. Some of these lectures may have required more than one class session to cover.


	LEC #				TOPICS


	1				Aerospace Dynamics (PDF - 1.1 MB)


	2				Coriolis "Demystified" (PDF - 2.4 MB)


	3				Dynamics (PDF - 1.3 MB)


	4				Introduction to Multiple Intermediate Frames (PDF)


	5				Momentum, Angular Momentum, and Dynamics of a System of Particles (PDF)


	6				Numerical Solution of Nonlinear Differential Equations (PDF - 1.4 MB)


	7				Lagrange's Equations (PDF)


	8				Examples Using Lagrange's Equations (PDF)


	9				Virtual Work and the Derivation of Lagrange's Equations (PDF)


	10				Friction in Lagrange's Equations (PDF)


	11				Kinematics of Rigid Bodies (PDF - 1.6 MB)


	12				Rigid Body Dynamics (PDF - 2.8 MB)


	13				Axisymmetric Rotations (PDF - 2.4 MB)


	14				Gyroscopes (PDF - 1.2 MB)


	15				Spacecraft Attitude Dynamics (PDF - 1.4 MB)


	16				Aircraft Dynamics (PDF)


	17				Aircraft Longitudinal Dynamics (PDF)


	18				Aircraft Lateral Dynamics (PDF - 1.5 MB)