- #1
Apashanka
- 429
- 15
In 2-D Cartesian coordinate system let's there exist a scaler field Φ(x1,x2) ,now we want to find how Φ changes with a curve which is described by the parameter(arc length) s
dΦ/ds=(∂Φ/∂xi)dxi/ds
Can we say for Cartesian coordinate system that along the curve at any s dxi always points in the same direction and hence dxi/ds
But for curvilinear coordinate system ,dxi points out in different direction for different s as the unit vector has no longer fixed direction for xi axis,
But how is dxi/ds pointing out tangentially to the curve at any s??
dΦ/ds=(∂Φ/∂xi)dxi/ds
Can we say for Cartesian coordinate system that along the curve at any s dxi always points in the same direction and hence dxi/ds
But for curvilinear coordinate system ,dxi points out in different direction for different s as the unit vector has no longer fixed direction for xi axis,
But how is dxi/ds pointing out tangentially to the curve at any s??