Engineering Dynamics

Lagrange Equations

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Session Overview

Covered this week: In week 8, we begin to use energy methods to find equations of motion for mechanical systems. We implement this technique using what are commonly known as Lagrange Equations, named after the French mathematician who derived the equations in the early 19th century. The method requires being able to express the kinetic and potential energies of rigid bodies, as well as the virtual work done by non-conservative external forces, referred to as generalized forces. Postage stamp of Joseph-Louis Lagrange to honor the French mathematician who derived the Lagrange equations. Public domain image.

Assignments

Handouts

• Lagrange Handout (PDF - 1.1MB)

Videos

Lecture Videos

• Watch Notation Systems

  • From this class forward, Prof. Vandiver uses a different notation system. Please watch this video to see how the different notation systems interrelate.

• Watch Lecture 15: Introduction to Lagrange With Examples

  • Video Chapters
    • Generalized coordinate definitions
    • Complete, independent and holonomic
    • Example problems

Recitation Video and Notes

• Watch Recitation 8: Cart and Pendulum, Lagrange Method
  • This recitation covers a Lagrange approach to a problem involving a cart and pendulum.
• Recitation 8 Notes: Cart and Pendulum (Lagrange) (PDF)
  • These recitation notes were compiled by Prof. David Gossard, another instructor for the course. His notes go over concepts and problems covered during the recitation sections he taught, and may not precisely correspond to the content covered in the above recitation video.

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