This short paper deals with a derivation of the three-dimensional Pythagorean Theorem employing the general equation of a circle. However, I am not presenting this paper with any kind of proofs or explanations for the concepts assisting the derivation of the Pythagorean Theorem.
As part of the NASA IMPACT program to model mechanical interactions with bodies in space such as comets, asteroids, and other Near Earth Objects (NEOs), the Colorado School of Mines team is designing a motor stage apparatus to interact with JSC-1A regolith simulant surfaces. This initial study involved development and testing of a prototype motor stage apparatus which was used to drive three types of probes into JSC-1A surfaces while collecting force data under standard Earth atmospheric conditions. The probes used were a conical-tipped probe, a wedge-tipped probe, and an anchoring probe. Main goals of the prototype system were to acquire general force trends for each interaction, and to isolate the most important design features for a more-complex in-vacuum system. Our data revealed force interactions that were very small in magnitude—on the order of tenths of Newtons—and more complex than our simple stiff beam probe and mount model could accurately predict. Our results lead us to recommend a more complex experimental model that can accurately represent deflection in the probes while also allowing for better measurement of regolith movement near the tip of the probes. Specifically, we recommend the following design features for the in-vacuum system: a load cell capable of measuring at very low ranges (thousandths of Newtons), reliability of structural axis alignment between trials, a robust mounting system that can accommodate each different type of probe, and consistency of sample preparation between trials.
Template for editors of a "contributed volume", provided by Springer, to help structure the manuscript, e.g., define the heading hierarchy. Predefined style formats are available for all the necessary structures that are supposed to be part of the manuscript.
The original template has been modified so that contribution from each author can be contained in their own folders, using the import package.
Note: These templates are not intended for the preparation of the final page layout! The final layout will be created by Springer according to their layout specifications.
This template satisfies the formatting requirements for Masters and Doctoral theses and dissertations from the College of Graduate Studies at the University of Idaho. It's easy to use and allows you to write each chapter as a separate tex document.