Project Description: Modern commercial airplanes are assembled out of millions of different parts. While many of these parts are rigid, many of them are not. For example, the hydraulic lines and flexible electrical conduits that supply an airplane's landing gear change their shape as the landing gear goes through its motion (you can see some of these lines in the accompanying photograph). These shapes can be modeled by minimizing the potential energy of the rest state of one of these flexible lines as the ends of the lines are moved by the landing gear. While this problem is amenable to solution through direct optimization of individual finite elements, the method often proves to be slow and unreliable. In this investigation, we will explore the use of variational methods (i.e. the calculus of variations) in an attempt to discover a more elegant and robust approach to modeling these flexible airplane parts. Reference: Any textbook on the calculus of variations. My favorite is The Variational Principles of Mechanics, by Cornelius Lanczos. Keywords: Geometrical modeling, calculus of variations, boundary value problems Prerequisites: Calculus of variations, optimization, numerical methods for ODEs and 2-point boundary value problems, Matlab