<Dd> e i (r) = lim ε → 0 r (x 1,..., x i + ε,..., x n) − r (x 1,..., x i,..., x n) ε, (\ displaystyle \ mathbf (e) _ (i) (\ mathbf (r)) = \ lim _ (\ epsilon \ rightarrow 0) (\ frac (\ mathbf (r) \ left (x ^ (1), \ \ dots, \ x ^ (i) + \ epsilon, \ \ dots, \ x ^ (n) \ right) - \ mathbf (r) \ left (x ^ (1), \ \ dots, \ x ^ (i), \ \ dots, \ x ^ (n) \ right)) (\ epsilon)) \,) i = 1,..., n (\ displaystyle i = 1, \ \ dots \, \ n \) </Dd> <P> which can be normalized to be of unit length . For more detail see curvilinear coordinates . </P> <P> Coordinate surfaces, coordinate lines, and basis vectors are components of a coordinate system . If the basis vectors are orthogonal at every point, the coordinate system is an orthogonal coordinate system . </P> <P> An important aspect of a coordinate system is its metric tensor g, which determines the arc length ds in the coordinate system in terms of its coordinates: </P>

Identify and describe motion relative to different frames of reference