1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Taking the time derivative of a curl

  1. Mar 18, 2015 #1
    Is the time derivative of a curl commutative? I think I may have answered this question.... Only the partial time derivative of a curl is commutative? The total time derivative is not, since for example in cartesian coordinates, x,y,and z can themselves be functions of time. In spherical and cylindrical coordinates, even the unit vectors depend on time? Also the partial derivative of a curl in curvilinear coordinates is commutative?
  2. jcsd
  3. Mar 19, 2015 #2


    User Avatar
    Science Advisor

    I think you are confusing coordinate variables (which are usually called x, y, z, t) with position variables (which are also usually called x, y, z, t). The difference is that coordinate variables refer to a fixed grid over which a vector field is defined, and position variables refer to some dynamic position of some object.

    A field has a value at each coordinate position, whereas an object only occupies a particular subset of coordinate positions. The time derivative and curl are commutative since they are operations on a field, and the field coordinates are (typically) orthogonal. It doesn't make sense to take the curl of an object position.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook