Generalized coordinates in Lagrangian mechanics

[ShayanJ]

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 want to know how will be the Lagrange's equations in such coordinates?
Could you give an example whose proper coordinates are as such?
Thanks

 

[Dale]

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.

 

[Killingtensor]

tbf, angles are dimensionless so there's no issue there.