Hence the typical Lagrange’s equation may be now written in the form
| d | ( | ∂Τ | ) − | ∂Τ | = − | ∂V | , |
| dt | ∂q˙r | ∂qr | ∂qr |
(13)
or, again,
| ṗr = − | ∂ | (V − Τ). |
| ∂qr |
(14)
It has been proposed by Helmholtz to give the name kinetic potential to the combination V − Τ.
As shown under [Mechanics], § 22, we derive from (10)
| dΤ | = Q1q˙1 + Q2q˙2 + ... , |
| dt |
(15)