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There are 4 modules in this course
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.
The material covered is taking from the book "Analytical Mechanics of Space Systems" available at https://arc.aiaa.org/doi/book/10.2514/4.105210.
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.
What's included
19 videos1 reading9 assignments
Show info about module content
19 videos•Total 158 minutes
Kinetics: Course Introduction•1 minute
Module 1 Introduction•1 minute
Overview of Kinetics•3 minutes
1: Continuous System Super Particle Theorem•13 minutes
2: Continuous System Kinetic Energy•9 minutes
3: Continuous System Linear Momentum•2 minutes
4: Continuous System Angular Momentum•8 minutes
Optional Review: Continuous Momentum and Energy Properties•19 minutes
5: Rigid Body Angular Momentum•7 minutes
6: Rigid Body Inertia Tensor•3 minutes
6.1: Rigid Body Inertia about Alternate Points•3 minutes
6.2: Rigid Body Inertia about Alternate Body Axes•6 minutes
7: Rigid Body Kinetic Energy•7 minutes
8: Rigid Body Equations of Motion•13 minutes
8.1: Integrating Rigid Body Equations of Motion•2 minutes
8.2 Example: Slender Rod Falling•20 minutes
(Tips for Solving Spring Particle Systems)•6 minutes
Optional Review: Rigid Body Properties•14 minutes
Optional Review: Rigid Body Equations of Motion•20 minutes
1 reading•Total 1 minute
Course Updates and Accessibility Support•1 minute
9 assignments•Total 174 minutes
Concept Check 1 - Super Particle Theorem•30 minutes
Concept Check 2 - Kinetic Energy•40 minutes
Concept Check 3 - Linear Momentum•5 minutes
Concept Check 4 - Angular Momentum•5 minutes
Concept Check 5 - Rigid Body Angular Momentum•10 minutes
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.
Concept Check 9 - Dual Spinner Linear Stability•25 minutes
Gravity Gradients
Module 3•2 hours to complete
Module details
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.
What's included
7 videos3 assignments
Show info about module content
7 videos•Total 77 minutes
Module 3 Introduction•1 minute
1: Gravity Gradient Torque Development•19 minutes
1.1: Gravity Gradient Torque in Body Frame•8 minutes
1.2: Gravity Gradient Net Spacecraft Force•10 minutes
Concept Check 3 - Gravity Gradient Linear Stability•30 minutes
Equations of Motion with Momentum Exchange Devices
Module 4•6 hours to complete
Module details
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).
What's included
7 videos4 assignments1 peer review
Show info about module content
7 videos•Total 95 minutes
Module 4 Introduction•1 minute
1: Introduction to Momentum Exchange Devices•3 minutes
1.2: Overview of Momentum Control Devices•16 minutes
2: VSCMG Equations of Motion Development•42 minutes
3: VSCMG Motor Torque Equations•8 minutes
4: VSCMG EOM Variations•9 minutes
Optional Review of Momentum Exchange Devices•15 minutes
4 assignments•Total 150 minutes
Concept Check 1 - Overview of Momentum Exchange Devices•30 minutes
Concept Check 2 - VSCMG Equations of Motion•60 minutes
Concept Check 3 - VSCMG Motor Torque Equations•30 minutes
Concept Check 4 - VSCMG EOM Variations•30 minutes
1 peer review•Total 120 minutes
Kinetics Final Assignment•120 minutes
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