Euler Lagrange Equations for 1 particle in 3-dimensions

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SUMMARY

The discussion centers on the application of Euler-Lagrange equations for a single particle in three-dimensional space. It is established that separate Euler-Lagrange equations can be formulated for each of the three orthogonal coordinates, and these equations do not need to sum to zero. The coordinates utilized in the equations are general coordinates and do not have to be orthogonal, allowing for flexibility in problem analysis. The inquiry also references the Taylor book on Classical Mechanics as a potential resource for further understanding.

PREREQUISITES
  • Understanding of Euler-Lagrange equations
  • Familiarity with classical mechanics principles
  • Knowledge of general coordinates in physics
  • Basic calculus, particularly partial derivatives
NEXT STEPS
  • Study the derivation and application of Euler-Lagrange equations in classical mechanics
  • Explore the concept of general coordinates and their implications in physics problems
  • Read the Taylor book on Classical Mechanics for deeper insights
  • Investigate non-orthogonal coordinate systems and their applications in mechanics
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This discussion is beneficial for physics students, educators, and anyone interested in classical mechanics, particularly those studying the Euler-Lagrange equations and their applications in multidimensional systems.

morangta
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Homework Statement


Do the Euler-Lagrange equations set to zero for each of the 3 orthogonal coordinates or do you sum them all equal to zero. Do the coordinates have to be orthogonal in order to write separate E-L equations? Or is there no such thing as non-orthogonal coordinates to analyze a problem? My main question is the first one.


Homework Equations


d/dt(partial L/partial qi dot) - (partial L/partial qi) = 0?


The Attempt at a Solution


Not sure. Self-study/No textbook here. Thank you for reading my question.
Would the Taylor book on Classical Mechanics explain this well?
 
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morangta said:

Homework Statement


Do the Euler-Lagrange equations set to zero for each of the 3 orthogonal coordinates or do you sum them all equal to zero.

You have separate equations for all coordinates. They are general coordinates, needn't be connected to spatial directions.


ehild
 

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