where
| arr = Σ [ m { ( | ∂x | )2 + ( | ∂y | )2 + ( | ∂z | )2 } ], |
| ∂qr | ∂qr | ∂qr |
| ars = Σ { m ( | ∂x | ∂x | + | ∂y | ∂y | + | ∂z | ∂z | ) } = asr. | |||
| ∂qr | ∂qs | ∂qr | ∂qs | ∂qr | ∂qs |
(2)
Thus T is expressed as a homogeneous quadratic function of the quantities q̇1, q̇2, ... q̇n, which are called the generalized components of velocity. The coefficients arr, ars are called the coefficients of inertia; they are not in general constants, being functions of the q’s and so variable with the configuration. Again, If (X, Y, Z) be the force on m, the work done in an infinitesimal change of configuration is
Σ (Xδx + Yδy + Zδz) = Q1δq1 + Q2δq2 + ... + Qnδqn,
(3)
where
| Qr = Σ ( X | ∂x | + Y | ∂y | + Z | ∂z | ). |
| ∂qr | ∂qr | ∂qr |
(4)