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.
Prof. Jonathan P. How
Prof. John Deyst
None required. Lecture notes will be handed out in class. But various books available for reference are:
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Meriam and Kraige. Engineering Mechanics - Dynamics. Wiley, 2001.
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Hibbeler. Engineering Mechanics - Statics and Dynamics. Prentice Hall.
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Beer and Johnston. Vector Mechanics for Engineers. McGraw-Hill.
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Greenwood. Principles of Dynamics. 2nd ed. Prentice Hall [RB dynamics].
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Williams, Jr. Fundamentals of Applied Dynamics. Wiley, 1996.
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Baruh. Analytical Dynamics. McGraw Hill [fairly advanced].
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Wells. Schaum's Outline of Lagrangian Dynamics. McGraw-Hill, 1967.
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Goldstein. Classical Mechanics. 2nd ed. Addison Wesley [very advanced].
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Derive the equations of motion in accelerating and rotating frames.
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Solve for the equations of motion using both the Newtonian and Lagrangian formulations.
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Simulate and predict complex dynamic behavior of vehicles such as projectiles, aircraft, and spacecraft.
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Use MATLAB® as a tool for matrix manipulations and dynamic simulation.
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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.
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| LEC # |
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| TOPICS |
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| ASSIGNMENTS |
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| 1 |
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| Aerospace Dynamics |
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| 2 |
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| Coriolis "Demystified" |
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| HW1 Issued |
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| 3 |
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| Dynamics |
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| 4 |
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| Introduction to Multiple Intermediate Frames |
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| HW1 Due
HW2 Issued |
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| 5 |
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| Momentum, Angular Momentum, and Dynamics of a System of Particles |
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| HW2 Due
HW3 Issued |
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| 6 |
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| Numerical Solution of Nonlinear Differential Equations |
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| HW3 Due |
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| Midterm Exam #1 |
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| 7 |
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| Lagrange's Equations |
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| 8 |
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| 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.) |
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| HW4 Issued |
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| 9 |
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| Virtual Work and the Derivation of Lagrange's Equations |
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| Virtual Work and the Derivation of Lagrange's Equations (Continued) |
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| HW4 Due
HW5 Issued |
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| 10 |
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| Friction in Lagrange's Equations |
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| Friction in Lagrange's Equations (Continued) |
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| HW5 Due
HW6 Issued |
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| 11 |
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| Kinematics of Rigid Bodies |
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| 12 |
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| Rigid Body Dynamics |
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| HW6 Due
HW7 Issued |
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| 13 |
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| Axisymmetric Rotations |
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| 14 |
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| Gyroscopes |
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| HW7 Due
HW8 Issued |
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| Gyroscopes (Continued) |
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| HW8 Due |
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| Midterm Exam #2 |
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| HW9 Issued |
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| 15 |
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| Spacecraft Attitude Dynamics |
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| Spacecraft Attitude Dynamics (Continued) |
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| HW9 Due
HW10 Issued |
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| 16 |
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| Aircraft Dynamics |
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| 17 |
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| Aircraft Longitudinal Dynamics |
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| HW10 Due |
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| 18 |
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| Aircraft Lateral Dynamics |
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| 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.
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| LEC # |
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| TOPICS |
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| 1 |
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| Aerospace Dynamics (PDF - 1.1 MB) |
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| 2 |
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| Coriolis "Demystified" (PDF - 2.4 MB) |
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| 3 |
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| Dynamics (PDF - 1.3 MB) |
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| 4 |
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| Introduction to Multiple Intermediate Frames (PDF) |
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| 5 |
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| Momentum, Angular Momentum, and Dynamics of a System of Particles (PDF) |
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| 6 |
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| Numerical Solution of Nonlinear Differential Equations (PDF - 1.4 MB) |
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| 7 |
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| Lagrange's Equations (PDF) |
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| 8 |
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| Examples Using Lagrange's Equations (PDF) |
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| 9 |
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| Virtual Work and the Derivation of Lagrange's Equations (PDF) |
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| 10 |
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| Friction in Lagrange's Equations (PDF) |
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| 11 |
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| Kinematics of Rigid Bodies (PDF - 1.6 MB) |
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| 12 |
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| Rigid Body Dynamics (PDF - 2.8 MB) |
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| 13 |
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| Axisymmetric Rotations (PDF - 2.4 MB) |
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| 14 |
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| Gyroscopes (PDF - 1.2 MB) |
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| 15 |
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| Spacecraft Attitude Dynamics (PDF - 1.4 MB) |
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| 16 |
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| Aircraft Dynamics (PDF) |
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| 17 |
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| Aircraft Longitudinal Dynamics (PDF) |
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| 18 |
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| Aircraft Lateral Dynamics (PDF - 1.5 MB) |
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