In a coordinate system given by ( x 1 , … , x N ) {\displaystyle \left(x_{1},\dots ,x_{N}\right)} the velocity and external force vectors u {\displaystyle \mathbf {u} } and g {\displaystyle \mathbf {g} } have components ( u 1 , … , u N ) {\displaystyle (u_{1},\dots ,u_{N})} and ( g 1 , … , g N ) {\displaystyle \left(g_{1},\dots ,g_{N}\right)} , respectively. Then the equations may be expressed in subscript notation as: