Space Vehicle Dynamics 🛰 Lecture 23: Dual-spin spacecraft can stabilize rotation about any principal axis. Why do we need this? For a rigid body (spacecraft) with no torques on it, rotation about the intermediate axis is unstable over very short time scales (the Intermediate Axis Theorem). Over longer time scales, rotation about the minimum axis is unstable due to energy dissipation (e.g. vibration of antennae or other structures). The only long term stable rotation state is rotation about the maximum inertia axis, which is a rotational kinetic energy minimum.
We discuss some historical satellite examples, then discuss the dual-spin approach for passively stabilizing a spacecraft spin about any principal axis, regardless of its inertia. A dual-spin spacecraft is a simple system where passive attitude stability is achieved by adding a single fly-wheel to the rigid spacecraft, spinning about the axis one wishes to stabilize. We go over the equations of motion and the necessary spin of the fly-wheel to achieve stability. Next time we will look at a numerical example.
► Next: Dual-Spin Spacecraft Stability Conditions
https://youtu.be/8uOxYf9nLNw
► Previous, Free Rigid Body Motion | Precession of Symmetric Bodies | General Motion
https://youtu.be/vtCrcVKpWC0
► More lectures posted regularly
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► Dr. Shane Ross 👨🏽🔬 aerospace engineering professor, Virginia Tech
Background: Caltech PhD | worked at NASA/JPL & Boeing
Research website for @Ross Dynamics Lab
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► Space Vehicle Dynamics course videos (playlist)
https://is.gd/SpaceVehicleDynamics
► Lecture notes (PDF)
https://is.gd/SpaceVehicleDynamicsNotes
► Chapters
0:00 Introduction | general rigid bodies, all principal axes different
2:30 Intermediate axis instability (Tennis Racket Theorem)
5:36 Phone toss, book toss to demonstrate 27:08 General free rigid body motion
10:00 Long-term instability of the minimum inertia axis
13:09 Historical space missions, learning lessons from failure
16:29 Dual-spin spacecraft stabilization
► References
Schaub & Junkins📘Analytical Mechanics of Space Systems, 4th edition, 2018
https://arc.aiaa.org/doi/book/10.2514/4.105210
► Topics covered in course https://is.gd/SpaceVehicleDynamics
- Typical reference frames in spacecraft dynamics
- Mission analysis basics: satellite geometry
- Kinematics of a single particle: rotating reference frames, transport theorem
- Dynamics of a single particle
- Multiparticle systems: kinematics and dynamics, definition of center of mass (c.o.m.)
- Multiparticle systems: motion decomposed into translational motion of c.o.m. and motion relative to the c.o.m.
- Multiparticle systems: imposing rigidity implies only motion relative to c.o.m. is rotation
- Rigid body: continuous mass systems and mass moments (total mass, c.o.m., moment of inertia tensor/matrix)
- Rigid body kinematics in 3D (rotation matrix and Euler angles)
- Rigid body dynamics; Newton's law for the translational motion and Euler’s rigid-body equations for the rotational motion
- Solving the Euler rotational differential equations of motion analytically in special cases
- Constants of motion: quantities conserved during motion, e.g., energy, momentum
- Visualization of a system’s motion
- Solving for motion computationally
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