Engineering Standards, Frames of Reference, and Conventions in .NET

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Engineering Standards, Frames of Reference, and Conventions
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Observer s Eyepoint
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Forward Direction of Observation
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Figure 45.1 Right-Handed Cartesian Coordinate System as an Observer s Frame of Reference
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Table 45.4 Examples of conventions applied to a 3-axis observer s frame of reference Item 45.1 45.2 45.3 Observation Object spatial position relative the observer s frame of reference Direction of movement relative to observer s frame of reference Translational movements about the observer s 3-axis frame of reference Directional Conventions Left, right, up, down Forward, backward, left, right, upward, and downward Rotations about an axis employing the Right-Hand Rule e.g., yaw, pitch, and roll
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YAW, PITCH, and ROLL Conventions. We can express translational motion about a 3-axis system by using the illustrations shown in Figure 45.2. Since the axes are different, we need to establish terms that enable us to differentiate motion. These terms are PITCH, YAW, and ROLL. For applications in which a frame of reference is allowed to rotate freely in any direction, we refer to it as a free body axis system. Table 45.5 lists descriptions of PITCH, YAW, and ROLL conventions applied a free body axis system. Guidepost 45.2 Our discussions up to this point provide generic descriptions of coordinate systems. Now let s explore some actual systems that implement these coordinate systems.
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World Coordinate System (WCS)
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Systems, such as land surveying, aircraft, and military troops, track their geospatial positions based on displacement of the origin of the MISSION SYSTEM relative to an Earth-based coordinate system. To do this, they establish a 3-axis frame of reference using the Earth s center as the origin. We refer to this system as the World Coordinate System (WCS) as illustrated in Figure 45.3. Whereas navigators employed magnetic compasses and sextants to determine geographic position with some level of accuracy, we navigate using the Global Positioning System (GPS) satellites located in Earth orbit. For the WCS:
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45.4 Coordinate Systems
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Plane of Rotation
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ROLL Angle Convention (Y rotates about X toward Z)
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Y Z X
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ROLL Axis of Rotation YAW Axis of Rotation
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PITCH Axis of Rotation
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Plane of Rotation
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Plane of Rotation
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PITCH Angle Convention (Z rotates about Y toward X)
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YAW Angle Convention (X rotates about Z toward Y)
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Figure 45.2 6 Degree of Freedom (DOF) Roll, Pitch, & Yaw Conventions
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Table 45.5 ROLL, PITCH, and YAW conventions for a right-handed, body-axis, cartesian coordinate system relative to the origin Parameter ROLL Convention Positive (+) ROLL Action Observeda Clockwise angular rotation about the longitudinal X-axis (i.e., along the direction of forward travel) in which the Y-axis rotates toward the Z-axis Counterclockwise angular rotation about the X-axis (Z into Y) Clockwise angular rotation about the Y-axis in which the Z-axis rotates toward the X-axis Counterclockwise angular rotation about the Y-axis (X into Z) Clockwise angular rotation about the Z-axis in which the X-axis rotates toward the Y-axis Counterclockwise angular rotation about the Z-axis (Y into X)
Negative (-) ROLL PITCH Positive (+) PITCH Negative (-) PITCH YAW Positive (+) YAW Negative (-) YAW
As viewed by an observer with their eye point located at the origin of a right-handed coordinate system.
1. The Z-axis extends from the center of the Earth (origin) through the North Pole. 2. The X-axis extends from the Earth s center (origin) through the Prime Meridian at the equator. 3. Finally, the Y-axis extends from the origin through 90 degrees East at the equator. Engineering computations and simulations employ models that require certain assumptions about the Earth s characteristics such as Earth Centered, Earth Fixed (ECEF); Earth Centered Rotating (ECR); and Earth Centered Inertial (ECI) models.
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Engineering Standards, Frames of Reference, and Conventions
Axis of Rotation
North Pole +Z
Prime Meridian (Greenwich)
90 Degrees East
Equator +X +Y
Figure 45.3 World Coordinate System (WCS) Application of the Right Hand Rule Rotation Convention
y2 x2
Y1 X1
Rotation
Figure 45.4 Frame of Reference Based Coordinate System
The WCS enables us to reference a speci c point on the surface of the Earth. But, HOW do air-based systems such as aircraft and spacecraft relate to the WCS Obviously, these systems employ on-board GPS technology. However, the systems are free bodies that are in motion relative to another body, the Earth, which is also in motion. HOW do we express their heading and rotational velocities and accelerations relative to their frame of reference
Free Body Dynamics Relative to a Fixed Body
Complex systems often require dynamic characterizations of a free body relative to another body that is assumed to be xed as illustrated in Figure 45.4. Where this is the case, select the coordinate system(s) to be applied to each body axis system. For this illustration, we establish an X1, Y1, Z1 coordinate system to represent the Earth s frame of reference and an X2, Y2, Z2 coordinate system to represent the orientation of a free body in space relative to the Earth.