Hey Kiwi_Dave.
As an educated guess, I would say to try and relate them to grad and div. These have very specific meanings:
Vector calculus identities - Wikipedia, the free encyclopedia
Given
then I can write the six partial derivatives (as I would when forming Euler-Lagrange equations):
,
or I can write the three partial derivatives
These two options use the same notation but give different things. How am I to know which is required? Does the notation mean that the derivatives are of the second kind?
Hey Kiwi_Dave.
As an educated guess, I would say to try and relate them to grad and div. These have very specific meanings:
Vector calculus identities - Wikipedia, the free encyclopedia
I think I have worked it out!
is the first type because of the way the Lagrangian is defined.
But is the second kind (Divergence) because the partial is being applied to a function that is not a Lagrangian.
Does that make sense?
Thanks Chiro, I am not entirely sure what you are driving at.
But I worry that I can write:
which turns my divergence back into a gradient problem, making my type two back into type 1.
Where this is coming from is that I am trying to calculate the divergence of the Hamiltonian tensor
Now I have a text book that shows me step by step how to do this. But in the first step they expand the partial of L like my type 2, they then cancel some terms but ultimately they seem to treat the partial of L like type 1 again. I have attached an image of my textbook page.