Uncovering the Lagrangian from Observations of Trajectories

Author: Berchenko-Kogan, Yakov Ilich

Year: 2011

Degree: Senior thesis (Minor)

Advisor: Desbrun, Mathieu

Committee Member: None, None

Option: Mathematics; Control and Dynamical Systems

DOI: 10.7907/4M31-DK09

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.

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