Скачать или смотреть Gravity Gradient, Part 2, Equilibrium Orientations

Space Vehicle Dynamics 🦕 Lecture 25: Gravity gradient, part 2. The gravity gradient torque can be written in terms of the moment of inertia matrix for a body in orbit. We introduce an orbit frame for a circular orbit, and express the gravity gradient torque in terms of a body-fixed frame, with special attention to a principal axis frame. We express the conditions for a relative equilibrium orientation, that is, the spacecraft keeps a constant attitude as viewed in the orbit frame (for example, always pointing an antenna at the Earth). The condition is that the principal axes of the body must be parallel to the orbit frame axes. But not all orientations are stable.

If perturbed from equilibrium, we can write the orientation of the satellite in terms of Euler angles of the body-frame with respect to the orbit frame, such as yaw, pitch, and roll. Assuming small angles, we can begin to write the equations of motion and determine the linear stability conditions, which we continue in the following lecture.

► Next: Gravity Gradient, Part 3, Stability Conditions, Frequencies, Torque Equilibrium Angle, Space Station
   • Gravity Gradient, Part 3, Stability Condit...  

► Previous, Gravity Gradients, Part 1, Deriving the Gravity Gradient Torque on a Body in Orbit
   • Gravity Gradient, Part 1, Deriving the Gra...  

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► Dr. Shane Ross 🤖 aerospace engineering professor, Virginia Tech
Background: Caltech PhD | worked at NASA/JPL & Boeing
Research website for ‪@ProfessorRoss‬

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► Space Vehicle Dynamics course videos (playlist)
   • Space Vehicle Dynamics  

► Lecture notes (PDF)
https://drive.google.com/drive/folder...

► References
Schaub & Junkins📘Analytical Mechanics of Space Systems, 4th edition, 2018
https://arc.aiaa.org/doi/book/10.2514...

► 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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