The quantities Qr are called the generalized components of force.

The equations of motion of m being

mẍ = X,   mÿ = Y,   mz̈ = Z,

(5)

we have

Σ { m ( ẍ ∂x+ ÿ ∂y+ z̈ ∂z) } = Qr.
∂qr ∂qr∂qr

(6)

Now

(7)

ẋ = ∂xq̇1 + ∂xq̇2 + ... + ∂xq̇n,
∂q1 ∂q2∂qn