To proceed, consider a single particle, and introduce the generalized coordinates as { q k } = (r, θ). Then Hildebrand shows in polar coordinates with the q k = (r, θ) the "generalized momenta" are: p r = m r ˙ ˙ , p θ θ = m r 2 θ θ ˙ ˙ , leading, for example, to the generalized force: d d t p r = Q r + m r θ θ ˙ ˙ 2 , with Q r the impressed radial force. The connection between "generalized forces" and Newtonian forces varies with the choice of coordinates. This Lagrangian formulation introduces exactly the "coordinate" form of fictitious forces mentioned above that allows "fictitious" (generalized) forces in inertial frames, for example, the term m r θ θ ˙ ˙ 2 . Careful reading of Hildebrand shows he doesn't discuss the role of "inertial frames of reference", and in fact, says "[The] presence or absence [of inertia forces] depends, not upon the particular problem at hand but upon the coordinate system chosen." By coordinate system presumably is meant the choice of { q k }. Later he says "If accelerations associated with generalized coordinates are to be of prime interest (as is usually the case), the [nonaccelerational] terms may be conveniently transferred to the right … and considered as additional (generalized) inertia forces. Such inertia forces are often said to be of the Coriolis type."