Let us determine the required roll-pitch-yaw angles(a, ß, y) to make the of the body coordinate B parallel to u(3, 4, 5), while y-axis remain in (X plane. Y yı 12 02 X X2 1₁ yı y2 X2 X1
Let us determine the required roll-pitch-yaw angles(a, ß, y) to make the of the body coordinate B parallel to u(3, 4, 5), while y-axis remain in (X plane. Y yı 12 02 X X2 1₁ yı y2 X2 X1
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Transcribed Image Text:**Text Transcription for Educational Website:**
Let us determine the required roll-pitch-yaw angles (\(\alpha, \beta, \gamma\)) to make the x-axis of the body coordinate B parallel to \(\mathbf{u}(3, 4, 5)\), while the y-axis remains in the (X, Y) plane.
**Diagram Explanation:**
The image shows two diagrams illustrating the rotation of a coordinate system. Each diagram includes:
1. A multi-segmented arm with joints labeled to show angles and axes.
2. The arms are color-coded in green, yellow, and blue segments.
3. Two rotation angles \(\theta_1\) and \(\theta_2\) are marked on each arm, indicating the rotation at each joint.
4. Axes labeled as \(X, Y, x_1, y_1, x_2, y_2\).
5. Distances labeled as \(l_1, l_2\) showing segment lengths.
6. The orientation of the x-axis is shown parallel to a given vector \(\mathbf{u}(3, 4, 5)\), while the y-axis is constrained within the (X, Y) plane in both diagrams.
These diagrams are intended to illustrate the process of aligning a local coordinate system with a global one through specific rotational transformations.
Expert Solution
Step 1
Imagine three lines intersecting at right angles at the center of gravity. Roll is the rotation of the front-to-back axis. Pitch refers to rotation around a side-to-side axis. Yaw is the rotation around the vertical axis.
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