Have you ever considered why we need to master Newton's laws in high school? What are the methods used by computers to solve differential equations? Is it related to Calculus in any way? Many educators agree that one of the most effective methods to engage students is to have them think about how they can apply what they've learned in the future. On June 25th, Professor Chia-Wei Hsu, an assistant professor of Electrical and Computer Engineering at the University of Southern California Viterbi School of Engineering, coached the SHINE students to solve a particular case of the Three-body problem using MATLAB programming.
The three-body problem is a classic physics problem that has captivated scientists' interests since Issac Newton's Universal Law of Gravitation was first stated in the 18th century. The Sun, the Earth, and the Moon make up our most familiar three-body system, and after thousands of years of research, we can now reliably predict their motion. However, most of the other three-body systems are still considered 'chaotic,' or in other words, not yet solvable(cite). Therefore, the mathematical difficulty of the problem has piqued the curiosity of both mathematicians and computer scientists for many years, with applications ranging from the earliest low-tech ship navigators to modern ideas of space travel.
Per annual custom, during the second week of the program SHINE students have started learning about MATLAB programming. They finished a guided training with Kendall Work, a senior at the University of Southern California studying Mechanical Engineering and a Microsoft intern, as well as the MathWorks Onramp seminars. The students were asked to use their MATLAB skills and develop simulations to visualize the Figure-8 Periodic solution to the problem during the three-body problem workshop. To support the students to make connections with their high school knowledge, Professor Hsu began by discussing a two-body problem, commonly taught in high school physics classes, before moving on to a more generic multi-body problem. He also introduced Euler's method and the Verlet velocity algorithm, two popular computational methods for solving the related equations.
A couple of students were successful in visualizing the motion of the items and requested a follow-up session to learn more about the subject. Accordingly, the students and Professor Hsu met again on June 29th to explore general applications of multi-body issues and how MATLAB and differential equations are employed in computational physics and electrical engineering. These skills and techniques taught by Professor Hsu today ready SHINE students for the engineering needs of tomorrow.
Published on July 9th, 2021
Last updated on August 13th, 2021