When do I need to use virtual work in writing the equations of motion?

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Discussion Overview

The discussion revolves around the application of the principle of virtual work in the context of Lagrangian dynamics, specifically regarding when it is necessary to incorporate virtual work into the equations of motion. Participants explore the relationship between the standard Euler-Lagrange equations and the modified equations that include non-conservative forces.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the necessity of using the principle of virtual work, suggesting that the standard form of the Euler-Lagrange equation implies that the difference should equal zero.
  • Another participant seeks clarification on the meaning of the term F sub q, indicating a need for precise definitions in the discussion.
  • A participant clarifies that q represents the generalized coordinate, providing an example with radial distance as a generalized coordinate.
  • It is proposed that the modified Euler-Lagrange equations are applicable when non-conservative forces are present, and that virtual work can be used to determine the non-conservative generalized forces.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and application of the principle of virtual work in the context of Lagrangian dynamics. The discussion remains unresolved regarding the conditions under which virtual work should be applied.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the applicability of the standard Euler-Lagrange equations versus the modified equations that include non-conservative forces. The definitions and implications of terms like F sub q are also not fully established.

jhosamelly
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I'm studying for our comprehensive exam . I just need to clarify something. So the equation of motion for lagrangian dynamics is [itex]\frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{i}}[/itex] = [itex]\frac{\partial L}{\partial {q}_{i}}[/itex]

However, in my notes there are example which uses the principle of virtual work wherein [itex]\frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{i}}[/itex] - [itex]\frac{\partial L}{\partial {q}_{i}}[/itex] = [itex]F_{q}[/itex]

Then we look for [itex]F_{q}[/itex] using virtual work.

However isn't [itex]\frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{i}}[/itex] - [itex]\frac{\partial L}{\partial {q}_{i}}[/itex] = 0 ?
 
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I think I can help you, but I don't want to answer without knowing what F sub q stands for just in case I make things worse. Can you specify what it represents please?
 
q is the generalized coordinate.

For example if I have r (radial distance) as generalized coordinate I'll have


[itex]\frac{d}{dt}\frac{\partial L}{\partial\dot{r}}[/itex] - [itex]\frac{\partial L}{\partial {r}}[/itex] = [itex]F_{r}[/itex]
 

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