Generalised coordinates

Generalised coordinates q₁, q₂, …, qₙ are any independent variables sufficient to pin down every configuration of a mechanical system. For a pendulum, a single angle θ is enough. For a double pendulum, two angles. For a bead sliding along a wire, the arc length. Cartesian position (x, y, z) is one legitimate choice, but almost never the most convenient.

The Lagrangian method works in ANY choice of generalised coordinates — this is its central strength. Constraints that would require explicit normal forces in a Newtonian free-body diagram disappear automatically when the constraint surface is the domain of the generalised coordinate.