Space Vehicle Dynamics ☀️ Lecture 14: Euler angle rates are not equal to the angular velocity. We derive the relationship between them carefully. We start with the fundamental kinematic differential equation for the direction cosine matrix [C]. By going through the successive pure rotations that define the Euler angles, we arrive at a matrix relationship between the Euler angles, yaw (ψ), pitch (θ), roll (Φ) in the 3-2-1 convention, and the angular velocity vector (ω) as seen in the body fixed frame. This is via a matrix we call [B], which depends on the Euler angles. We also discuss the singularity problem of the Euler angles. This suggests we search for other alternative ways to represent rotations based on the principal rotation vector.
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► Dr. Shane Ross 🛩aerospace engineering professor, Virginia Tech
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► References
Schaub & Junkins, Analytical Mechanics of Space Systems, 4th edition, 2018
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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
► Courses & Playlists by Dr. Ross
▶️ 3-Body Problem Orbital Dynamics
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▶️ Space Manifolds
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▶️ Space Vehicle Dynamics
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▶️ Lagrangian & 3D Rigid Body Dynamics
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▶️ Nonlinear Dynamics & Chaos
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▶️ Hamiltonian Dynamics
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▶️ Center Manifolds, Normal Forms, & Bifurcations
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Негізгі бет Euler Angle Rates & Angular Velocity- Kinematic Differential Equation for Rigid Body Dynamics
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