Coordinate Systems in .NET

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45.4 Coordinate Systems
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Conventional Right-Handed Coordinate (Z-Axis Up) Z
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Rotated Right-Handed Coordinate (Z-Axis Down)
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Gravitational Loading Effects Result in NEGATIVE Quantities Gravitational Loading Effects Result in POSITIVE Quantities
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Figure 45.5 Engineering Statics and Mechanics Conventions
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Six Degree of Freedom (6 DOF) Models. A free body in space has a relative position within the base frame of reference. Within that space its travels in any direction can be translated into motion relative to the X-, Y-, or Z-axes. It can also freely rotate about the axes of its own frame of reference. As such, we label this type of system as having six degrees of freedom (6 DOF). State Vectors. The 6 DOF discussion also provides the basis for the concept of state vectors. State vectors enable us to express the relative heading, velocities, and accelerations about the axes of a free body in space.
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Applications of Coordinate Systems and Conventions to Engineering Mechanics
The preceding discussions illustrate the basic concept of standard right-handed Cartesian coordinate system as illustrated at the left side of Figure 45.5. For many applications this convention is acceptable. However, from an engineering mechanics perspective, the establishment of the positive Z-axis pointing upward means that analysis of gravity-based loading effects result in negative Z components. For systems with this challenge, we can facilitate computation by rotating the 3-axis system so that the positive Z-axis points downward toward the center of the Earth. To illustrate this application, consider NASA s Space Shuttle example shown at the right side of Figure 45.6. Here the X-axis represents the forward direction of travel; the Y-axis extends from the center of gravity (CG) through the right wing. Now consider the added complexity in which the Shuttle maneuvers in orbit to y UPSIDE DOWN and BACKWARD during most of its mission to. 1. Minimize the thermal and radiation effects of the sun by turning the vehicle s belly toward the Sun and using the heat tiles as a solar shield.
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Engineering Standards, Frames of Reference, and Conventions
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Right-Hand Rule Rotation Convention +Z
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YAW Rotation Convention
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Positive Roll Positive Ya w Positive Pitch
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ROLL Rotation Convention
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+Y + + +Y
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Space Shuttle Application
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Forward Direction of Observation
Figure 45.6 Space Shuttle Coordinate System Application
2. Minimize the impact areas of orbital debris and meteorites that may cross its path that could damage tiles on the vehicle s nose or leading edges of the wings. 3. Shield Cargo Bay equipment from impacts that could damage dangerous or fragile instruments. 4. Minimize the energy required to deploy payloads. 5. Slow the vehicle for reentry by ring small nozzles, which are located on the rear of the vehicle, in the direction of forward travel. Guidepost 45.3 The preceding discussions relate to a free body operating as a MISSION SYSTEM relative to another free body. Now let s shift our attention to focus on the MISSION SYSTEM as an integrated set of components that must interface as an integrated framework. This leads to the next question: How do we reference a system consisting of multiple components that are integrated to form the free body system
Dimensional Reference Coordinate Systems
One of the challenges in the engineering of systems is expressing the relative position and orientation of physically integrated components within the system. The objective is to ensure they interoperate in form, t, and function and individually do not interfere with each other unintentionally, or have a negative impact on the performance of the system, its operators, and its facilities or mission objectives. This challenge requires positioning integrated components in a virtual frame of reference or structure and attaching them at integration points (IPs) or nodes to ensure interoperability. Then, identifying additional attachment points such as lift points that enable external systems to lift or move the integrated system. This requires establishing a dimensional coordinate system. NASA s Space Shuttle coordinate system shown in Figure 45.7 provides an excellent example of a dimensional coordinate system. Here, the Orbiter Vehicle (OV), External Tank (ET), and Solid
45.4 Coordinate Systems
Subscripts T = External Tank B = Solid Rocket Booster 0 = Orbiter S = Shuttle System FRL = Fuselage Reference Line