<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> <Dl> <Dd> (d s) 2 = g i k d x i d x k, (\ displaystyle (ds) ^ (2) = g_ (ik) \ dx ^ (i) \ dx ^ (k) \,) </Dd> </Dl> <Dd> (d s) 2 = g i k d x i d x k, (\ displaystyle (ds) ^ (2) = g_ (ik) \ dx ^ (i) \ dx ^ (k) \,) </Dd>

Why is it important to specify a reference point for describing motion