Lagrange's Equations: Know When to Use Each

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SUMMARY

Lagrange's equations are critical in classical mechanics for analyzing systems with constraints. The equation of the first kind, ∂L/∂q - (d/dt)(∂L/∂q̇) = Q, is applicable when non-conservative forces are present, while the Euler-Lagrange equation, ∂L/∂q - (d/dt)(∂L/∂q̇) = 0, is specifically for conservative forces. Understanding when to apply each equation is essential for accurate modeling of physical systems. The discussion highlights the importance of recognizing the nature of forces involved in the system.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with differential equations
  • Knowledge of conservative and non-conservative forces
  • Basic proficiency in calculus
NEXT STEPS
  • Study the derivation of Lagrange's equations in classical mechanics
  • Learn about conservative vs. non-conservative forces in physics
  • Explore applications of Lagrange's equations in real-world problems
  • Investigate advanced topics such as Hamiltonian mechanics
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Students and professionals in physics, engineers working on dynamic systems, and anyone interested in advanced mechanics will benefit from this discussion.

Isaac0427
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Lagrange's equation of the first kind gives us ∂L/∂q-(d/dt)(∂L/∂q.)=Q and the Euler-Lagrange equations give us ∂L/∂q-(d/dt)(∂L/∂q.)=0 (I know the equations are not perfectly written but you get the point). How do you know which one to use?
 
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The second one only account for conservative forces. When you have forces that ain't conservative the right side is the sum of these forces.
(Assuming I understood your notation correctly, been a long time since I did this)

Edit: maybe someone else can give their input, after checking it again I suspect I may have give you a (way) too simplistic answer.
 
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