1 / 14

Calculus of Variation and Euler-Lagrange Equation Lecture #4

Calculus of Variation and Euler-Lagrange Equation Lecture #4. Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical and Computer Engineering Department, University of Louisville, Louisville, KY, USA

cutter
Télécharger la présentation

Calculus of Variation and Euler-Lagrange Equation Lecture #4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Calculus of Variation and Euler-Lagrange EquationLecture #4 Hossam Abdelmunim1 & Aly A. Farag2 1Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2Electerical and Computer Engineering Department, University of Louisville, Louisville, KY, USA ECE 643 – Fall 2010

  2. Our Problem Formulation • Our problem formulation is based on finding a variable/function that minimizes a given energy. So, our target is to find: Maximization will be straightforward by finding the minimization of –F. Euler-Lagrange equations help us solve this problem.

  3. 1D Euler-Lagrange

  4. 1D Euler-Lagrange (Cont…)

  5. 1D Euler-Lagrange (Cont…)

  6. 1D Euler-Lagrange (Cont…)

  7. 1D Euler-Lagrange (Cont…) This is called Euler-Lagrange equation. It is obvious that our target to solve for ɸ for minimization.

  8. Euler-Lagrange equation for Many Independent and Higher Order Derivatives of One Dependent Variable and More

  9. Euler-Lagrange equation for Many Independent and Higher Order Derivatives of One Dependent Variable and More (Cont…)

  10. Euler-Lagrange equation for Many Independent and Higher Order Derivatives of One Dependent Variable and More (Cont…)

  11. Euler-Lagrange equation for Many Independent and Higher Order Derivatives of One Dependent Variable and More (Cont…)

  12. Euler-Lagrange equation for Many Independent and Higher Order Derivatives of More Than One Dependent Variable and More (Cont…)

  13. Euler-Lagrange and the Gradient Descent

  14. Euler-Lagrange and the Gradient Descent(Cont…)

More Related