About this course: The movement of bodies in space (like spacecraft, satellites, and space stations) must be predicted and controlled with precision in order to ensure safety and efficacy. Kinematics is a field that develops descriptions and predictions of the motion of these bodies in 3D space. This course in Kinematics covers four major topic areas: an introduction to particle kinematics, a deep dive into rigid body kinematics in two parts (starting with classic descriptions of motion using the directional cosine matrix and Euler angles, and concluding with a review of modern descriptors like quaternions and Classical and Modified Rodrigues parameters). The course ends with a look at static attitude determination, using modern algorithms to predict and execute relative orientations of bodies in space. After this course, you will be able to... * Differentiate a vector as seen by another rotating frame and derive frame dependent velocity and acceleration vectors * Apply the Transport Theorem to solve kinematic particle problems and translate between various sets of attitude descriptions * Add and subtract relative attitude descriptions and integrate those descriptions numerically to predict orientations over time * Derive the fundamental attitude coordinate properties of rigid bodies and determine attitude from a series of heading measurements
Who is this class for: This class is for working engineering professionals looking to add to their skill sets, graduate students in engineering looking to fill gaps in their knowledge base, and enterprising engineering undergraduates looking to expand their horizons.
Taught by: Hanspeter Schaub, Alfred T. and Betty E. Look Professor of Engineering
Department of Aerospace Engineering Sciences
| Level | Advanced |
| Commitment | Best completed in 4 weeks, with a commitment of between 3 and 6 hours of work per week. |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
- Video: Professor Introduction
- Video: Kinematics Course Introduction
- Video: Module One: Particle Kinematics Introduction
- Video: 1: Particle Kinematics
- Video: Optional Review: Vectors, Angular Velocities, Coordinate Frames
- Video: 2: Angular Velocity Vector
- Video: 3: Vector Differentiation
- Video: 3.1: Examples of Vector Differentiation
- Video: 3.2: Example of Planar Particle Kinematics with the Transport Theorem
- Video: 3.3: Example of 3D Particle Kinematics with the Transport Theorem
- Video: Optional Review: Angular Velocities, Coordinate Frames, and Vector Differentiation
- Video: Optional Review: Angular Velocity Derivative
- Video: Optional Review: Time Derivatives of Vectors, Matrix Representations of Vector
- Video: Module Two: Rigid Body Kinematics Part 1 Introduction
- Video: 1: Introduction to Rigid Body Kinematics
- Video: 2: Directional Cosine Matrices: Definitions
- Reading: Eigenvector Review
- Video: 3: DCM Properties
- Video: 4: DCM Addition and Subtraction
- Video: 5: DCM Differential Kinematic Equations
- Video: Optional Review: Tilde Matrix Properties
- Video: Optional Review: Rigid Body Kinematics and DCMs
- Video: 6: Euler Angle Definition
- Video: 7: Euler Angle / DCM Relation
- Video: 7.1: Example: Topographic Frame DCM Development
- Video: 8: Euler Angle Addition and Subtraction
- Video: 9: Euler Angle Differential Kinematic Equations
- Video: 10: Symmetric Euler Angle Addition
- Video: Optional Review: Euler Angle Definitions
- Video: Optional Review: Euler Angle Mapping to DCMs
- Video: Optional Review: Euler Angle Differential Kinematic Equations
- Video: Optional Review: Integrating Differential Kinematic Equations
- Video: Module Three: Rigid Body Kinematics Part 2 Introduction
- Video: 1: Principal Rotation Parameter Definition
- Video: 2: PRV Relation to DCM
- Video: 3: PRV Properties
- Video: Optional Review: Principal Rotation Parameters
- Video: 4: Euler Parameter (Quaternion) Definition
- Video: 5: Mapping PRV to EPs
- Video: 6: EP Relationship to DCM
- Video: 7: Euler Parameter Addition
- Video: 8: EP Differential Kinematic Equations
- Video: Optional Review: Euler Parameters and Quaternions
- Video: 9: Classical Rodrigues Parameters Definitions
- Video: 10: CRP Stereographic Projection
- Video: 11: CRP Relation to DCM
- Video: 12: CRP Addition and Subtraction
- Video: 13: CRP Differential Kinematic Equations
- Video: 14: CRPs through Cayley Transform
- Video: Optional Review: CRP Properties
- Video: 15: Modified Rodrigues Parameters Definitions
- Video: 16: MRP Stereographic Projection
- Video: 17: MRP Shadow Set Property
- Video: 18: MRP to DCM Relation
- Video: 19: MRP Addition and Subtraction
- Video: 20: MRP Differential Kinematic Equation
- Video: 21: MRP Form of the Cayley Transform
- Video: Optional Review: MRP Definitions
- Video: Optional Review: MRP Properties
- Video: 22: Stereographic Orientation Parameters Definitions
- Video: Optional Review: SOPs
- Video: Module Four: Static Attitude Determination Introduction
- Video: 1: Attitude Determination Problem Statement
- Video: 2: TRIAD Method Definition
- Video: 2.1: TRIAD Method Numerical Example
- Video: 3: Wahba's Problem Definition
- Video: 4: Devenport's q-Method
- Video: 4.1: Example of Devenport's q-Method
- Video: 5: QUEST
- Video: 5.1: Example of QUEST
- Video: 6: Optimal Linear Attitude Estimator
- Video: 6.1: Example of OLAE
- Video: Optional Review: Attitude Determination
- Video: Optional Review: Attitude Estimation Algorithms
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One of the best courses that I have ever done in coursera. Schaub can explain advanced concepts in a very pragmatic and easy-to-understand way. Suggested for professionals already with a Master degree's in Engineering, or student with solid basis of Geometry and Mathematical Programming (e.g. Matlab, Mathematica)
This is a great course for working through the book, "Analytical Mechanics of Space Systems" that I've owned for many years but never got around to working through it at the level of detail involved in working through the problems on paper, instead of just in my head. Prof Schaub does an excellent job of filling in the gaps in the text and making it more understandable, but it does really, really help to have the book to work through along with the class. Even with a background in physics, math, and engineering, I immediately learned something new about how to solve kinematics problems that I should have known but didn't. The concept of generalized/canonical coordinate systems never made sense to me until this class, where for some reason the explanation just clicked and I knew how it worked like flipping a switch. That knowledge alone was worth the price of the certificate. Continuing on to work the follow-on courses and perhaps complete the specialization.
wonderful course. very interesting
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Great Course! Given the advanced nature of this subject, Prof Schaub has successfully carved out an extremely neat course structure. His lectures provide valuable and clear insights into the concepts at play. The assignments are thorough and engaging as well. This course has already added substantial value to my background in Aerospace. I'm looking forward to enrolling in other similar courses!