What is the fastest route down a hill? (Spring 2024)


The project is an introduction to optimizing the time traveled along a curve from one point to another lower point further away. The field is called ``calculus of variations."  Students will have the opportunity to work on simplified optimal design problems, whose focus will  be on solving ordinary differential equations, using properties of curves studied in Calculus III, and building experimental models. The project will introduce students to useful insights in mathematical modeling as well as give a gentle introduction to higher-level mathematical investigations.


The brachistochrone problem (from Greek Brachistos = shortest and chronos = time), first proposed by Johann Bernoulli in 1696 and considered the birth of the calculus of variations, consists of finding a descent trajectory traced by a frictionless body moving from a point A to a lower point B in the quickest time possible. Since then, the brachistochrone problem has had major applications, such as optimal design in sports and road engineering, optics and kinematic, to name a few. From the mathematical point of view, the shortest time problem produces curves and surfaces with special properties. In this project, several problems involving brachistochrone-like solutions will be presented and investigated collaboratively.



For more information contact Thialita Nascimento (thnasc@iastate.edu) or Soumyajit Saha (ssaha1@iastate.edu)

People:


Pre-requisites: