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Author template for Management Science (mnsc) for articles with e-companion (EC)
Mirko Janc, Ph.D., INFORMS, mirko.janc@informs.org
ver. 0.95, December 2010
The density of solid water, unlike most molecules, is less than that of its liquid form. Its precise value is of use in many applications. Freezing a spherical droplet of water and analyzing the changed shape from a sphere to a sphere with a slight peak in order to find the density of ice. We find the density of ice to be at 0.90 ± 1.66 · 106 g/mL. The precision of our measurement was limited by uncertainty in the angle measurements of the peak of the droplet.
In this paper we will study an algorithm designed by Madgwick which is commonly used to determine the orientation of a quadcopter. The algorithm uses a group of accelerometers, gyroscopes and magnetometers integrated in what is called an IMU as input. Some differences have been found between the results obtained by the original paper and the implementation done by the author. Therefore, a thorough study has been made, finding a miscalculation in the equations. The results show a relative average error in the orientation of 1,44 ppm.
A proof is given that the summation of all prime numbers can be assigned the value of 13/12, as well as values that can be assigned to the summation of all multiples and all odd multiples.
A simple example of creating a list of acronyms using the acronym package, which supports auto-expansion on first mention, and shortening on subsequent mentions.