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.
This course is part of the Spacecraft Dynamics and Control Specialization
Offered By
Spacecraft Dynamics and Control SpecializationUniversity of Colorado BoulderAbout this Course
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Course 2 of 4 in the
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Advanced Level
Approx. 21 hours to complete
English
Subtitles: French, Portuguese (European), Russian, English, Spanish
Learner Career Outcomes
50%
started a new career after completing these courses
50%
got a tangible career benefit from this course
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Course 2 of 4 in the
Flexible deadlines
Reset deadlines in accordance to your schedule.
Advanced Level
Approx. 21 hours to complete
English
Subtitles: French, Portuguese (European), Russian, English, Spanish
Offered by
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.
Syllabus - What you will learn from this course
6 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.
6 hours to complete
19 videos (Total 158 min)
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 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
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
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
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.
2 hours to complete
7 videos (Total 77 min)
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 Stability30m
6 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).
6 hours to complete
7 videos (Total 95 min)
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 Devices30m
Concept Check 2 - VSCMG Equations of Motion1h
Concept Check 3 - VSCMG Motor Torque Equations30m
Concept Check 4 - VSCMG EOM Variations30m
Reviews
TOP REVIEWS FROM KINETICS: STUDYING SPACECRAFT MOTION
by RSAug 16, 2020
Great teacher, great course. I recommend studying with the book since it's not an easy topic. The first course was a bit better since there were more programming exercises to train.
by JPSep 22, 2020
A good course to understand concept and practical evaluation process to useit on field.
by HJul 20, 2020
It's hard, but you learn a lot. Mr Schaub is great teacher.
by MKAug 28, 2020
great lectures highly recommended for space enthusiasts
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.
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