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Uncovering the Lagrangian from Observations of Trajectories


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


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.

Item Type:Thesis (Senior thesis (Minor))
Subject Keywords:Lagrangian ; control and dynamical systems
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mathematics
Minor Option:Control and Dynamical Systems
Awards:Upper Class Merit Prize (Rosalind W. Alcott Merit Scholarship, Carnation Scholarship, and John Stauffer Merit Scholarship), 2009. Axline Merit Scholars, 2008-2010. Herbert J. Ryser Memorial Scholarships, 2010. Scott Russell Johnson Undergraduate Mathematics Prize, 2011.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Desbrun, Mathieu
Thesis Committee:
  • None, None
Defense Date:1 June 2011
Record Number:CaltechTHESIS:10162015-141215167
Persistent URL:
Berchenko-Kogan, Yakov Ilich0000-0002-4987-3254
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9224
Deposited By: Kathy Johnson
Deposited On:16 Oct 2015 23:19
Last Modified:09 Oct 2019 17:11

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