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From Researcher to Award Winner: Eric Montag ’17

Aug 03, 2017

8/3/17

Eric Montag class of 2017Randolph-Macon College alumnus Eric Montag '17 won an award for a paper he presented at the annual meeting of the Virginia Academy of Science (VAS), which was held May 17-19, 2017 at Virginia Commonwealth University. Montag's paper, which was based on research he did under the joint supervision of R-MC Mathematics Professor Adrian Rice and mentor Dr. Roland Bowles '58, won the Carpenter Award for the Best Student Presentation.

Montag also gave a presentation on his research at the national meeting of Pi Mu Epsilon, the national mathematics honor society, at Mathfest, the summer meeting of the Mathematical Association of America, which took place July 26-29, 2017 in Chicago, Illinois.

"My number one goal in presenting my research is to convey the details of my year-long research project," says Montag, who will soon began working at the Naval Surface Warfare Center Dahlgren division, where he will conduct research on lasers.

The Research
Montag majored in physics and mathematics and minored in engineering physics at R-MC. Two Schapiro Undergraduate Research Fellowship (SURF) projects that he did helped fuel his interest in research. The SURF program offers students the opportunity to conduct 10 weeks of full-time, original research, under the mentorship of a faculty mentor.

"We started off with a basic problem in which we wanted to be able to find a way to mathematically model the rotations of a rigid body in 3-dimensional space, for example a satellite orbiting the earth," explains Montag. "The biggest challenge in solving this problem was that we needed our method to be able to model any rotation without any singularities, i.e. points at which the method fails. Another constraint was that, for maximum efficiency, we wanted our model to have the minimum number of necessary parameters, i.e. independent mathematical components that form the basis of the model."

Four Approaches
In fall 2016, Montag studied four different approaches, three of which were 3-parameter models: Euler Angles (which use sines and cosines), Cayley Transformations (which use matrices), and Rodrigues' Formula (which uses vectors). He then found a paper which proved that no 3-parameter method could produce the results we wanted, so he turned to his fourth approach, a 4-parameter method called Quaternions, which are a 4-dimensional extension of an algebraic concept known as complex numbers. This method did effectively model 3D rotations without singularities.

"This actually solved our initial problem, but in spring 2017 we returned to our 3-parameter methods, and tried to work out the connections between them," explains Montag. "We did this by going back to the original mathematical papers of Arthur Cayley, Olinde Rodrigues, and William Hamilton from the 1840s, as well as Leonhard Euler's original work on the subject from the 1770s. We ended up proving quite a neat little result: namely that, although they look very different and involve different mathematical concepts, the 3- and 4-parameter methods of our study all turn out to be inherently equivalent."

Mentorship + Gratitude
Throughout his research, Montag met often with Bowles, an aerospace researcher who worked at NASA Langley Research Center from 1960-1996 in a variety of research and management positions. Currently a NASA DRA (Distinguished Research Associate), his research is focused on aircraft-generated wake vortices as related to aviation safety.

"Dr. Bowles' experience in mathematical physics came in very handy," says Montag.  "His experience in the field is amazing. I also met with Professor Rice, who made sure I stayed on track and read over the work that Dr. Bowles and I were doing. Professor Rice's ability to write mathematics and his knowledge of math history were invaluable to my research. It’s my hope that in a couple of years my research will be published."

Bowles earned his B.S. in physics and mathematics at R-MC, his M.S. in physics at University of Richmond, and his Ph.D. in applied mathematics at University of Virginia.

"It was a great joy working with Eric," says Bowles. "During the course of this project, Eric demonstrated an excellent grasp of the required subject matter, as well as an impressive command of necessary mathematical and computational techniques. Eric's work ethic and commitment to detail throughout this research project were exemplary."

During his R-MC tenure, Montag also presented papers at the American Physical Society, the American Physical Society South Eastern Section, the American Association of Physics Teachers, and multiple Research Day events and SURF symposia.

"My physics and mathematics professors helped me immensely throughout my career at R-MC," he says. "I cannot state enough how much gratitude I have for Dr. Bowles and Professor Rice for their guidance. In addition, Physics Professor Rachele Dominguez helped me realize my passion for research and applied mathematics."