Uncovering the Lagrangian from Observations of Trajectories

Uncovering the Lagrangian from Observations of Trajectories

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 numeric...

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Main Author: Berchenko-Kogan, Yakov Ilich
Format: Others
Published: 2011
Online Access:https://thesis.library.caltech.edu/9224/1/uncoveringlagrangianfinal.pdf
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 <https://resolver.caltech.edu/CaltechTHESIS:10162015-141215167>
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spelling ndltd-CALTECH-oai-thesis.library.caltech.edu-92242019-10-10T03:02:40Z Uncovering the Lagrangian from Observations of Trajectories Berchenko-Kogan, Yakov Ilich 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. 2011 Thesis NonPeerReviewed application/pdf https://thesis.library.caltech.edu/9224/1/uncoveringlagrangianfinal.pdf https://resolver.caltech.edu/CaltechTHESIS:10162015-141215167 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 <https://resolver.caltech.edu/CaltechTHESIS:10162015-141215167> https://thesis.library.caltech.edu/9224/
collection NDLTD
format Others
sources NDLTD
description 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.
author Berchenko-Kogan, Yakov Ilich
spellingShingle Berchenko-Kogan, Yakov Ilich
Uncovering the Lagrangian from Observations of Trajectories
author_facet Berchenko-Kogan, Yakov Ilich
author_sort Berchenko-Kogan, Yakov Ilich
title Uncovering the Lagrangian from Observations of Trajectories
title_short Uncovering the Lagrangian from Observations of Trajectories
title_full Uncovering the Lagrangian from Observations of Trajectories
title_fullStr Uncovering the Lagrangian from Observations of Trajectories
title_full_unstemmed Uncovering the Lagrangian from Observations of Trajectories
title_sort uncovering the lagrangian from observations of trajectories
publishDate 2011
url https://thesis.library.caltech.edu/9224/1/uncoveringlagrangianfinal.pdf
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 <https://resolver.caltech.edu/CaltechTHESIS:10162015-141215167>
work_keys_str_mv AT berchenkokoganyakovilich uncoveringthelagrangianfromobservationsoftrajectories
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