Space Vehicle Dynamics 🚀 Lecture 13: Euler angles. Illustration of why you want to know the direction cosine matrix [C]; to track where an instrument is pointing on a satellite relative to an Earth-centered inertial frame. The kinematic differential equation gives how [C] changes with time. Parameterizing [C] with Euler angles, e.g., yaw-pitch-roll, a sequence of pure rotations. [C] is then a product of three rotation matrices. More general Euler angles; there are 12 sets or conventions. Yaw (ψ), pitch (θ), roll (Φ) is the 3-2-1 convention. The 3-1-3 convention is used for Keplerian orbital elements; longitude of the ascending node (Ω), inclination (i), argument of periapsis (ω).
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► Dr. Shane Ross 🛩aerospace engineering professor, Virginia Tech
Background: Caltech PhD | worked at NASA/JPL & Boeing
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► Lecture notes (PDF)
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► All course videos (playlist)
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► References
Schaub & Junkins, Analytical Mechanics of Space Systems, 4th edition, 2018
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Yaw-pitch-roll 3-2-1 Euler angle video
• The Aerospace Euler An...
3-1-3 Euler angle video
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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 (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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Негізгі бет Euler Angles for Aerospace | Yaw, Pitch, Roll
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