Σm(ẋδx + ẏδy + z˙δz) = A11q˙1 + A12q˙2 + ...)δq1 + (A21q˙1 + A22q˙2 + ...)δq2 + ...,
(6)
where
| Arr = Σm { ( | ∂x | ) | ² | + ( | ∂y | ) | ² | + ( | ∂z | ) | ² | }, |
| ∂qr | ∂qr | ∂qr |
(7)
| Ars = Σm { | ∂x | ∂x | + | ∂y | ∂y | + | ∂z | ∂z | } = Asr. |
| ∂qr | ∂qs | ∂qr | ∂qs | ∂qr | ∂qs |
If we form the expression for the kinetic energy Τ of the system, we find
2Τ = Σm(ẋ² + ẏ² + z˙²) = A11q˙1² + A22q˙2² ... 2A12q˙1q˙2 + ...
(8)
The coefficients A11, A22, ... A12, ... are by an obvious analogy called the coefficients of inertia of the system; they are in general functions of the co-ordinates q1, q2,.... The equation (6) may now be written