Space Vehicle Dynamics 🛰 Lecture 22: The torque-free motion of an axisymmetric rigid body, that is, a rigid body with two principal moments of inertia which are equal. We analyze the motion of the symmetric free rigid body viewed in the body-fixed frame and inertial frame. Then we cover torque-free motion of an arbitrary rigid body, that is, a rigid body with all principal moments of inertia different. The motion is understood in terms of conserved quantities: the rotational kinetic energy is conserved and so is the magnitude of the angular momentum. So in the 3D phase space of the body-fixed angular momentum components, the motion must be at the intersection of an energy ellipsoid and momentum sphere.
CORRECTION at 12:57, there should be an I_3 in front of ω_3 in the 3rd entry of the H_c vector
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► Dr. Shane Ross 👨🏽🏫 aerospace engineering professor, Virginia Tech
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► Chapters
0:00 Introduction
1:18 Torque-free motion of axisymmetric rigid bodies
21:30 Body and space cones
27:08 General free rigid body motion
► References
Schaub & Junkins📘Analytical Mechanics of Space Systems, 4th edition, 2018
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Kasdin & Paley📕 Engineering Dynamics: A Comprehensive Introduction
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► Topics covered in course is.gd/SpaceVeh...
- 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
- Rigid body dynamics
- 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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Негізгі бет Free Rigid Body Motion | Precession of Symmetric Bodies | General Motion
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