Euler Lagrange Equations for 1 particle in 3-dimensions

[morangta]

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?

 

[ehild]

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