This course is part of the Spacecraft Dynamics and Control Specialization

4.8
stars
122 ratings

Hanspeter Schaub

9,513 already enrolled

Offered By

Spacecraft Dynamics and Control SpecializationUniversity of Colorado Boulder

About this Course

6,574 recent views

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.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Course 2 of 4 in the

Spacecraft Dynamics and Control Specialization

Advanced Level

Approx. 21 hours to complete

English

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Course 2 of 4 in the

Spacecraft Dynamics and Control Specialization

Advanced Level

Approx. 21 hours to complete

English

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

Instructor

Instructor rating

4.88/5 (25 Ratings)

Hanspeter Schaub

Glenn L. Murphy Chair in Engineering, Professor

Department of Aerospace Engineering Sciences

28,423 Learners

7 Courses

Offered by

University of Colorado Boulder

See how employees at top companies are mastering in-demand skills

Learn more about Coursera for Business

Syllabus - What you will learn from this course

Week

Week 1

6 hours to complete

Continuous Systems and Rigid Bodies

6 hours to complete

19 videos (Total 158 min)

19 videos

Kinetics: Course Introduction1m

Module 1 Introduction53s

Overview of Kinetics2m

1: Continuous System Super Particle Theorem13m

2: Continuous System Kinetic Energy9m

3: Continuous System Linear Momentum2m

4: Continuous System Angular Momentum7m

Optional Review: Continuous Momentum and Energy Properties19m

5: Rigid Body Angular Momentum6m

6: Rigid Body Inertia Tensor3m

6.1: Rigid Body Inertia about Alternate Points3m

6.2: Rigid Body Inertia about Alternate Body Axes6m

7: Rigid Body Kinetic Energy6m

8: Rigid Body Equations of Motion13m

8.1: Integrating Rigid Body Equations of Motion1m

8.2 Example: Slender Rod Falling19m

(Tips for Solving Spring Particle Systems)5m

Optional Review: Rigid Body Properties14m

Optional Review: Rigid Body Equations of Motion19m

9 practice exercises

Concept Check 1 - Super Particle Theorem30m

Concept Check 2 - Kinetic Energy40m

Concept Check 3 - Linear Momentum5m

Concept Check 4 - Angular Momentum5m

Concept Check 5 - Rigid Body Angular Momentum10m

Concept Check 6 - Parallel Axis Theorem6m

Concept Check 6.1 - Coordinate Transformation30m

Concept Check 7 - Kinetic Energy8m

Concept Check 8 - Equations of Motion40m

Week

Week 2

7 hours to complete

Torque Free Motion

The motion of a single or dual rigid body system is explored when no external torques are acting on it. Large scale tumbling motions are studied through polhode plots, while analytical rate solutions are explored for axi-symmetric and general spacecraft shapes. Finally, the dual-spinner dynamical system illustrates how the associated gyroscopics can be exploited to stabilize any principal axis spin.

7 hours to complete

17 videos (Total 166 min)

17 videos

Module 2 Introduction1m

1: Torque Free Motion Polhode Plots33m

1.1 Example: Special Polhode Plots3m

2: Torque Free Motion Axisymmetric Solution5m

3: Torque Free Motion General Inertia Case14m

4: Torque Free Motion Integrals of Motion6m

5: Torque Free Motion Phase Space Plots9m

5 Example: Phase Space Plots for Varying Energy Levels4m

6: Torque Free Motion Attitude Precession11m

6 Example: Phase Space Plot of Duffing Equation4m

Optional Review: Torque Free Motion10m

7: Dual Spinner Equations of Motion11m

8: Dual Spinner Spin Equilibria7m

9: Dual Spinner Linear Stability11m

9 Example: Dual Spinner Stability10m

9.1: Spin Up Considerations13m

Optional Review: Dual Spinner EOM and Equilibria7m

9 practice exercises

Concept Check 1 - Rigid Body Polhode Plots30m

Concept Check 2 - Torque Free Motion with Axisymmetric Body30m

Concept Check 3 - Torque Free Motion General Inertia1h 10m

Concept Check 4 - Torque Free Motion Integrals of Motion30m

Concept Check 5 - Torque Free Motion Phase Space Plots30m

Concept Check 6 - Torque Free Motion Precession15m

Concept Check 7 - Dual Spinner Equations of Motion15m

Concept Check 8 - Dual Spinner Equilibria30m

Concept Check 9 - Dual Spinner Linear Stability25m

Week

Week 3

2 hours to complete

Gravity Gradients

2 hours to complete

7 videos (Total 77 min)

7 videos

Module 3 Introduction1m

1: Gravity Gradient Torque Development19m

1.1: Gravity Gradient Torque in Body Frame7m

1.2: Gravity Gradient Net Spacecraft Force9m

2: Gravity Gradient Relative Equilibria Orientations10m

3: Gravity Gradient Linear Stability about Equilibria22m

Extra Example: Gravity Gradient Polar Pear Mission5m

3 practice exercises

Concept Check 1 - Gravity Gradient Derivation15m

Concept Check 2 - Gravity Gradient Equilibria6m

Concept Check 3 - Gravity Gradient Linear Stability30m

Week

Week 4

6 hours to complete

Equations of Motion with Momentum Exchange Devices

6 hours to complete

7 videos (Total 95 min)

7 videos

Module 4 Introduction1m

1: Introduction to Momentum Exchange Devices2m

1.2: Overview of Momentum Control Devices16m

2: VSCMG Equations of Motion Development41m

3: VSCMG Motor Torque Equations8m

4: VSCMG EOM Variations9m

Optional Review of Momentum Exchange Devices15m

4 practice exercises

Concept Check 1 - Overview of Momentum Exchange Devices30m

Concept Check 2 - VSCMG Equations of Motion1h

Concept Check 3 - VSCMG Motor Torque Equations30m

Concept Check 4 - VSCMG EOM Variations30m

Reviews

4.8

28 reviews

5 stars
84.42%
4 stars
13.93%
3 stars
1.63%

TOP REVIEWS FROM KINETICS: STUDYING SPACECRAFT MOTION

by JPSep 22, 2020

A good course to understand concept and practical evaluation process to useit on field.

by OMApr 30, 2021

Great course, interesting and well taught.

For future updates to the course my suggestion is to give a computational example regarding the material covered in week 4

by RPAug 24, 2021

Good course. Buying the book by Prof. Schaub will help you a lot in succeeding in this course.

by NBFeb 25, 2019

excellent course content with knowledgeable professor. Challenging to learn and focused on both analytical theory and practical example.

View all reviews

About the Spacecraft Dynamics and Control Specialization

Spacecraft Dynamics and Control covers three core topic areas: the description of the motion and rates of motion of rigid bodies (Kinematics), developing the equations of motion that prediction the movement of rigid bodies taking into account mass, torque, and inertia (Kinetics), and finally non-linear controls to program specific orientations and achieve precise aiming goals in three-dimensional space (Control). The specialization invites learners to develop competency in these three areas through targeted content delivery, continuous concept reinforcement, and project applications.

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I subscribe to this Specialization?
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

More questions? Visit the Learner Help Center.

Build employee skills, drive business results

Discover Coursera for Business

Kinetics: Studying Spacecraft Motion

About this Course