Uncovering the Lagrangian from Observations of Trajectories

Citation

Berchenko-Kogan, Yakov Ilich (2011) Uncovering the Lagrangian from Observations of Trajectories. Senior thesis (Minor), California Institute of Technology. doi:10.7907/4M31-DK09. https://resolver.caltech.edu/CaltechTHESIS:10162015-141215167

Abstract

We approach the problem of automatically modeling a mechanical system from data about its dynamics, using a method motivated by variational integrators. We write the discrete Lagrangian as a quadratic polynomial with varying coefficients, and then use the discrete Euler-Lagrange equations to numerically solve for the values of these coefficients near the data points. This method correctly modeled the Lagrangian of a simple harmonic oscillator and a simple pendulum, even with significant measurement noise added to the trajectories.

Thesis Files