Question: Extract term from Lie derivative

Hi;

To compute higher-order lie derivatives we need to pass a vector field to LieDerivative(..) function. What follows is the result of LieDerivative(..) command:

 

To compute 2nd-order lie derivative we should first create a vector field as follows:

L1fh := ((1/2)*(x+u)*(-2*y+2*x)/sqrt((y-x)^2+L^2))*D_x + ((1/2)*(y+v)*(2*y-2*x)/sqrt((y-x)^2+L^2))*D_y + (L^2/sqrt((y-x)^2+L^2))*D_L;

 

Is there a function to extraxt components of an expression which is the result of the LieDerivative(..)? For example how we can extract the first term. i.e. :

 

 

sample code:


with(DifferentialGeometry):


DGsetup([x, y, L], R3);

h := sqrt((y-x)^2 + L^2);
 
f := evalDG((x+u)*D_x + (y+v)*D_y + L*D_L);

L1fh := LieDerivative(f, h);

simplify(L1fh);
       
L2fh := LieDerivative(L1fh, h);


L1fh := ((1/2)*(x+u)*(-2*y+2*x)/sqrt((y-x)^2+L^2))*D_x + ((1/2)*(y+v)*(2*y-2*x)/sqrt((y-x)^2+L^2))*D_y + (L^2/sqrt((y-x)^2+L^2))*D_L;

L2fh := LieDerivative(L1fh, h);


simplify(L2fh);


 

Please Wait...