About this Specialization
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100% online courses

Start instantly and learn at your own schedule.
Flexible Schedule

Flexible Schedule

Set and maintain flexible deadlines.
Advanced Level

Advanced Level

Knowledge of vector calculus, linear algebra, particle dynamics, fixed axis rotation, and basic spring-mass-damper stability

Hours to complete

Approx. 6 months to complete

Suggested 5 hours/week
Available languages

English

Subtitles: English...

What you will learn

  • Check

    Apply transport theorem to differentiate vectors, derive frame dependent velocity and acceleration vectors, and solve kinematic particle problems,

  • Check

    Translate between sets of attitude descriptions; add and subtract relative attitude descriptions for the movement of rigid bodies

  • Check

    Apply the static stability conditions of a dual-spinner configuration to derive equations of motion for rigid bodies with momentum exchange devices

  • Check

    Apply Lyapunov method to argue stability and convergence on a range of systems, analyze rigid body control convergence with unmodeled torque

Skills you will gain

kinematicsattitude dynamicskineticscontrol of nonlinear attitudespacecraft motion
100% online courses

100% online courses

Start instantly and learn at your own schedule.
Flexible Schedule

Flexible Schedule

Set and maintain flexible deadlines.
Advanced Level

Advanced Level

Knowledge of vector calculus, linear algebra, particle dynamics, fixed axis rotation, and basic spring-mass-damper stability

Hours to complete

Approx. 6 months to complete

Suggested 5 hours/week
Available languages

English

Subtitles: English...

How the Specialization Works

Take Courses

A Coursera Specialization is a series of courses that helps you master a skill. To begin, enroll in the Specialization directly, or review its courses and choose the one you'd like to start with. When you subscribe to a course that is part of a Specialization, you’re automatically subscribed to the full Specialization. It’s okay to complete just one course — you can pause your learning or end your subscription at any time. Visit your learner dashboard to track your course enrollments and your progress.

Hands-on Project

Every Specialization includes a hands-on project. You'll need to successfully finish the project(s) to complete the Specialization and earn your certificate. If the Specialization includes a separate course for the hands-on project, you'll need to finish each of the other courses before you can start it.

Earn a Certificate

When you finish every course and complete the hands-on project, you'll earn a Certificate that you can share with prospective employers and your professional network.

how it works

There are 4 Courses in this Specialization

Course1

Kinematics: Describing the Motions of Spacecraft

4.9
41 ratings
14 reviews
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...
Course2

Kinetics: Studying Spacecraft Motion

4.9
15 ratings
4 reviews
As they tumble through space, objects like spacecraft move in dynamical ways. Understanding and predicting the equations that represent that motion is critical to the safety and efficacy of spacecraft mission development. Kinetics: Modeling the Motions of Spacecraft trains your skills in topics like rigid body angular momentum and kinetic energy expression shown in a coordinate frame agnostic manner, single and dual rigid body systems tumbling without the forces of external torque, how differential gravity across a rigid body is approximated to the first order to study disturbances in both the attitude and orbital motion, and how these systems change when general momentum exchange devices are introduced. After this course, you will be able to... *Derive from basic angular momentum formulation the rotational equations of motion and predict and determine torque-free motion equilibria and associated stabilities * Develop equations of motion for a rigid body with multiple spinning components and derive and apply the gravity gradient torque * Apply the static stability conditions of a dual-spinner configuration and predict changes as momentum exchange devices are introduced * Derive equations of motion for systems in which various momentum exchange devices are present Please note: this is an advanced course, best suited for working engineers or students with college-level knowledge in mathematics and physics....
Course3

Control of Nonlinear Spacecraft Attitude Motion

4.8
23 ratings
4 reviews
This course trains you in the skills needed to program specific orientation and achieve precise aiming goals for spacecraft moving through three dimensional space. First, we cover stability definitions of nonlinear dynamical systems, covering the difference between local and global stability. We then analyze and apply Lyapunov's Direct Method to prove these stability properties, and develop a nonlinear 3-axis attitude pointing control law using Lyapunov theory. Finally, we look at alternate feedback control laws and closed loop dynamics. After this course, you will be able to... * Differentiate between a range of nonlinear stability concepts * Apply Lyapunov’s direct method to argue stability and convergence on a range of dynamical systems * Develop rate and attitude error measures for a 3-axis attitude control using Lyapunov theory * Analyze rigid body control convergence with unmodeled torque...
Course4

Spacecraft Dynamics Capstone: Mars Mission

The goal of this capstone spacecraft dynamics project is to employ the skills developed in the rigid body Kinematics, Kinetics and Control courses. An exciting two-spacecraft mission to Mars is considered where a primary mother craft is in communication with a daughter vehicle in another orbit. The challenges include determining the kinematics of the orbit frame and several desired reference frames, numerically simulating the attitude dynamics of the spacecraft in orbit, and implementing a feedback control that then drives different spacecraft body frames to a range of mission modes including sun pointing for power generation, nadir pointing for science gathering, mother spacecraft pointing for communication and data transfer. Finally, an integrated mission simulation is developed that implements these attitude modes and explores the resulting autonomous closed-loop performance. Tasks 1 and 2 use three-dimensional kinematics to create the mission related orbit simulation and the associated orbit frames. The introductory step ensures the satellite is undergoing the correct motion, and that the orbit frame orientation relative to the planet is being properly evaluated. Tasks 3 through 5 create the required attitude reference frame for the three attitude pointing modes called sun-pointing, nadir-pointing and GMO-pointing. The reference attitude frame is a critical component to ensure the feedback control drives the satellite to the desired orientation. The control employed remains the same for all three pointing modes, but the performance is different because different attitude reference frames are employed. Tasks 6 through 7 create simulation routines to first evaluate the attitude tracking error between a body-fixed frame and a particular reference frame of the current attitude mode. Next the inertial attitude dynamics is evaluated through a numerical simulation to be able to numerically analyze the control performance. Tasks 8-11 simulate the closed-loop attitude performance for the three attitude modes. Tasks 8 through 10 first simulate a single attitude at a time, while tasks 11 develops a comprehensive attitude mission simulation which considers the attitude modes switching autonomously as a function of the spacecraft location relative to the planet....

Instructor

Avatar

Hanspeter Schaub

Glenn L. Murphy Chair of Engineering, Professor
Department of Aerospace Engineering Sciences

About University of Colorado Boulder

CU-Boulder is a dynamic community of scholars and learners on one of the most spectacular college campuses in the country. As one of 34 U.S. public institutions in the prestigious Association of American Universities (AAU), we have a proud tradition of academic excellence, with five Nobel laureates and more than 50 members of prestigious academic academies....

Frequently Asked Questions

  • Yes! To get started, click the course card that interests you and enroll. You can enroll and complete the course to earn a shareable certificate, or you can audit it to view the course materials for free. When you subscribe to a course that is part of a Specialization, you’re automatically subscribed to the full Specialization. Visit your learner dashboard to track your progress.

  • This course is completely online, so there’s no need to show up to a classroom in person. You can access your lectures, readings and assignments anytime and anywhere via the web or your mobile device.

  • This Specialization doesn't carry university credit, but some universities may choose to accept Specialization Certificates for credit. Check with your institution to learn more.

  • While it is recommended to take the specialization in the order Kinematics, Kinetics, Control, Capstone Mission, it is not a hard requirement.

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