code: def rect_to_cyl_vec(vx,vy,vz,X,Y,Z,cyl=False):
      
      if not cyl:
          R,phi,Z= rect_to_cyl(X,Y,Z)
      else:
          phi= Y
      vr=+vx*sc.cos(phi)+vy*sc.sin(phi)
      vt= -vx*sc.sin(phi)+vy*sc.cos(phi)
      return (vr,vt,vz)
docs: NAME:
  
         rect_to_cyl_vec
  
      PURPOSE:
  
         transform vectors from rectangular to cylindrical coordinates vectors
  
      INPUT:
  
         vx - 
  
         vy - 
  
         vz - 
  
         X - X
  
         Y - Y
  
         Z - Z
  
         cyl - if True, X,Y,Z are already cylindrical
  
      OUTPUT:
  
         vR,vT,vz
  
      HISTORY:
  
         2010-09-24 - Written - Bovy (NYU)