L - Lie derivative

Lv1, v2, v3..., vn[expr]
L[v1, v2, v3..., vn, expr]
allows one to calculate the Lie derivative on an expression along given vector field
  • expr - any expression (on which Lie derivative is defined). v1, v2, v3..., vn - vector fields.
  • The derivative has the following properties:
  • - For any vector fields X1, X2, .., Xn and expression a we have: LX1, X2, .., Xn(a)=LX1(LX2(..LXn(a)))
  • - For any vector field X and 0-form f we have: Lx(f)=X(d(f))
  • - For vector fields X and Y we have: Lx(Y)=[X, Y]
  • - For any vector field X and tensor fields and T the Leibniz rule for the Lie derivative takes place: LX(T)=(LX())T+(LX(T))
  • - For any vector field X and p-form we have: LX()=X(d())+d(X())