## Generalized coordinates in Lagrangian mechanics

In some texts about Lagrangian mechanics,its written that the generalized coordinates need not be length and angles(as is usual in coordinate systems)but they also can be quantities with other dimensions,say,energy,$length^2$ or even dimensionless.
I wanna know how will be the Lagrange's equations in such coordinates?
Could you give an example whose proper coordinates are as such?
Thanks

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 Mentor Lagranges equations are unchanged regardless of the units of the coordinates. You can take any problem with lengths and angles and simply do an arbitrary change of variables to get a coordinate in any units you like. E.g. Take any length and divide by the speed of light and you have a new coordinate with units of time.
 tbf, angles are dimensionless so there's no issue there.