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Abstract Upper-division undergraduate physics coursework necessitates a firm grasp on and fluid use of mathematical knowledge, including an understanding of non-cartesian (specifically polar, spherical and cylindrical) coordinates and how to use them. A limited body of research into physics students’ thinking about coordinate systems suggests that even for upper-division students, understanding of coordinate system concepts is emergent. To more fully grasp upper-division physics students’ incoming understanding of non-cartesian coordinates, the prevalence of non-cartesian content in seven popular Calculus textbooks was studied. Using content analysis techniques, a coding scheme was developed to gain insight into the presentation of coordinate system content both quantitatively and qualitatively. An initial finding was that non-cartesian basis unit vectors were absent in all but one book. A deeper analysis of three of the calculus textbooks showed that cartesian coordinates comprise an overwhelming proportion of the textbooks’ content and that qualitatively the cartesian coordinate system is presented as the default coordinate system. Quantitative and qualitative results are presented with implications for how these results might impact physics teaching and research at the middle and upper-division.
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Path Planning in the Local-Level Frame for Small Unmanned Aircraft Systems
In this chapter, we propose a 3D path planning algorithm for small unmanned aircraft systems (UASs). We develop the path planning logic using a body fixed relative coordinate system which is the unrolled, unpitched body frame. In this relative coordinate system, the ownship is fixed at the center of the coordinate system, and the detected intruder is located at a relative position and moves with a relative velocity with respect to the ownship. This technique eliminates the need to translate the sensor’s measurements from local coordinates to global coordinates, which saves computation cost and removes the error introduced by the transformation. We demonstrate and validate this approach using predesigned encounter scenarios in the Matlab/Simulink environment.
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- Award ID(s):
- 1650547
- PAR ID:
- 10053364
- Date Published:
- Journal Name:
- InTech
- ISSN:
- 0192-303X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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