About this Course
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Advanced Level

Approx. 24 hours to complete

Suggested: Best completed in 4 weeks, with a commitment of between 2 and 5 hours of work per week....

English

Subtitles: English

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Advanced Level

Approx. 24 hours to complete

Suggested: Best completed in 4 weeks, with a commitment of between 2 and 5 hours of work per week....

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
5 hours to complete

Continuous Systems and Rigid Bodies

The dynamical equations of motion are developed using classical Eulerian and Newtonian mechanics. Emphasis is placed on rigid body angular momentum and kinetic energy expression that are shown in a coordinate frame agnostic manner. The development begins with deformable shapes (continuous systems) which are then frozen into rigid objects, and the associated equations are thus simplified.

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19 videos (Total 158 min), 9 quizzes
19 videos
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 Theorem6m
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 Transformation8m
Concept Check 7 - Kinetic Energy8m
Concept Check 8 - Equations of Motion40m
Week
2
5 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.

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17 videos (Total 166 min), 9 quizzes
17 videos
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 Plots18m
Concept Check 2 - Torque Free Motion with Axisymmetric Body4m
Concept Check 3 - Torque Free Motion General Inertia1h 10m
Concept Check 4 - Torque Free Motion Integrals of Motion2m
Concept Check 5 - Torque Free Motion Phase Space Plots2m
Concept Check 6 - Torque Free Motion Precession15m
Concept Check 7 - Dual Spinner Equations of Motion15m
Concept Check 8 - Dual Spinner Equilibria6m
Concept Check 9 - Dual Spinner Linear Stability25m
Week
3
2 hours to complete

Gravity Gradients

The differential gravity across a rigid body is approximated to the first order to study how it disturbs both the attitude and orbital motion. The gravity gradient relative equilibria conditions are derived, whose stability is analyzed through linearization.

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7 videos (Total 77 min), 3 quizzes
7 videos
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 Stability2m
Week
4
5 hours to complete

Equations of Motion with Momentum Exchange Devices

The equations of motion of a rigid body are developed with general momentum exchange devices included. The development begins with looking at variable speed control moment gyros (VSCMG), which are then specialized to classical single-gimbal control moment devices (CMGs) and reaction wheels (RW).

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7 videos (Total 95 min), 5 quizzes
7 videos
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 Devices14m
Concept Check 2 - VSCMG Equations of Motion1h
Concept Check 3 - VSCMG Motor Torque Equations6m
Concept Check 4 - VSCMG EOM Variations6m
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Top reviews from Kinetics: Studying Spacecraft Motion

By NBFeb 26th 2019

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

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....

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. The goal of the specialization is to introduce the theories related to spacecraft dynamics and control. This includes the three-dimensional description of orientation, creating the dynamical rotation models, as well as the feedback control development to achieve desired attitude trajectories....
Spacecraft Dynamics and Control

Frequently Asked Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • 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.

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