δA = ∫t′t δΤdt + ∫t′t Σm (ẋδẋ + ẏδẏ + z˙δz˙) dt + 2Τ′δt′ − 2Τδt
= ∫t′t δΤdt + [ Σm (ẋδx + ẏδy + z˙δz)]t′t
− ∫t′t Σm (ẍδx + ÿδy + z¨δz) dt + 2Τ′δt′ − 2Τδt.
(4)
Now, by d’Alembert’s principle,
Σm (ẍδx + ÿδy + z¨δz) = −δV,
(5)
and by hypothesis we have
δ(Τ + V) = 0.
(6)