Point Transformations in the Lagrangian

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SUMMARY

This discussion focuses on the effects of time-independent point transformations on the Lagrangian in classical mechanics. The user seeks clarification on the covariance and contravariance of values resulting from these transformations. The conversation highlights the importance of correctly formulating the equations involved, particularly in understanding the relationship between the left and right sides of the equations presented. The user expresses uncertainty regarding the derivation of specific factors in the equations.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with point transformations
  • Knowledge of covariance and contravariance in physics
  • Basic proficiency in mathematical formulations of physical equations
NEXT STEPS
  • Study the principles of time-independent point transformations in Lagrangian mechanics
  • Research covariance and contravariance in the context of classical mechanics
  • Examine detailed examples of Lagrangian formulations
  • Explore advanced topics in differential geometry related to transformations
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Students and researchers in physics, particularly those focused on classical mechanics and theoretical physics, will benefit from this discussion.

dynamicskillingme
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Homework Statement


Hi, I'm working on understanding how a time independent point transformation
gif.gif
. effects the Lagrangian and to see how what values are co and contra variant.

Homework Equations


Would these be correct formulations, or have I overlooked something?

The Attempt at a Solution


gif.gif

and
gif.gif

for Q = 0, from
gif.gif
 
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dynamicskillingme said:
rtial%20L%7D%7B%5Cpartial%20q%7D%20%29%20%5Cfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20q*%7D%3D%200.gif
The left side seems ok. I don't know where the right side comes from, I mean the second factor of the left side.
 

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