Engineering Dynamics

Lagrange Equations Continued

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Session Overview

Covered this week: In week 9, we continue to study Lagrange equations with an emphasis on finding generalized forces. The shape of this bubble corresponds to a solution of the Lagrange equations. Image courtesy of whologwhy on Flickr.

Assignments

Problems and Concept Questions

Each problem set has concept questions paired with most problems. Answers to the concept questions are handed in before the overall problem set is due. You should therefore answer the concept questions in each problem set while watching the video lectures for the week. Then, use the Concept Question Answer Key (below in the Check Yourself section) to check your work before continuing to work on the problem set.

Please note that if your answer to the concept question is incorrect, it is likely that you may start down an unproductive pathway to a solution. Try to fully understand the answer to the concept question before you begin the regular problem.

• Problem Set 7: Problems and Concept Questions (PDF)

Videos

Lecture Videos

• Watch Lecture 16: Kinematic Approach to Finding Generalized Forces

  • Video Chapters
    • Concept question discussion
    • Kinematic approach to finding generalized forces Example of a wheel on moving cart with an incline
    • Mass sliding on rod example

• Watch Lecture 17: Practice Finding EOM Using Lagrange Equations

  • Video Chapters
    • New formula for computing torque about moving points
    • Example of hockey puck with a pull string-direct method
    • Hockey puck by Lagrange
    • Condensing many forces to one force and one moment at center of mass
    • Generic pendulum by Lagrange
    • Examples: Atwood’s machine and falling stick

Recitation Video and Notes

• Watch Recitation 9: Generalized Forces
  • This recitation covers generalized forces in a double pendulum. Questions about the upcoming quiz are also addressed.
• Recitation 9 Notes: Generalized Forces with Double Pendulum Example (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.

Check Yourself

Concept Question Answer Key and Problem Set Solutions

The solutions are presented in two files, one with the answers to the concept questions, and one with solutions and in-depth explanations for the problems. Work the problems on your own and check your answers when you’re done.

• Problem Set 7: Concept Question Answer Key (PDF)
• Problem Set 7: Problem Solutions and Explanations (PDF)

Looking for something specific in this course? The Resource Index compiles links to most course resources in a single page.

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