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#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 22 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.

#### Approx. 22 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
4 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....
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 Energy8m
Concept Check 3 - Linear Momentum2m
Concept Check 4 - Angular Momentum4m
Concept Check 5 - Rigid Body Angular Momentum8m
Concept Check 6 - Parallel Axis Theorem2m
Concept Check 6.1 - Coordinate Transformation8m
Concept Check 7 - Kinetic Energy4m
Concept Check 8 - Equations of Motion20m
Week
2
4 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....
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 Inertia14m
Concept Check 4 - Torque Free Motion Integrals of Motion2m
Concept Check 5 - Torque Free Motion Phase Space Plots2m
Concept Check 6 - Torque Free Motion Precession2m
Concept Check 7 - Dual Spinner Equations of Motion2m
Concept Check 8 - Dual Spinner Equilibria6m
Concept Check 9 - Dual Spinner Linear Stability10m
Week
3
2 hours to complete

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. ...
7 videos (Total 77 min), 3 quizzes
7 videos
1.1: Gravity Gradient Torque in Body Frame7m
1.2: Gravity Gradient Net Spacecraft Force9m
2: Gravity Gradient Relative Equilibria Orientations10m
Extra Example: Gravity Gradient Polar Pear Mission5m
3 practice exercises
Concept Check 1 - Gravity Gradient Derivation12m
Concept Check 2 - Gravity Gradient Equilibria4m
Concept Check 3 - Gravity Gradient Linear Stability2m
Week
4
4 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)....
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 Motion10m
Concept Check 3 - VSCMG Motor Torque Equations6m
Concept Check 4 - VSCMG EOM Variations6m

## Instructor

### Hanspeter Schaub

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

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....