Recent content by eipiplusone

(hopefully, the equations display now). I don't see anything about the Ad-map in Pantheon-link - am I missing something? Regarding Ado's theorem. As I understand it, it can be used to show that any finite dimensional Lie group is locally isomorphic to a Linear group (a matrix group). I guess...

Hi, let ##G## be a Lie group, ##\varrho## its Lie algebra, and consider the adjoint operatores, ##Ad : G \times \varrho \to \varrho##, ##ad: \varrho \times \varrho \to \varrho##. In a paper (https://aip.scitation.org/doi/full/10.1063/1.4893357) the following formula is used. Let ##g(t)## be a...

Thank you. The documents you link to looks very nice, I will see if they can make things clear to me.

Thanks for your answer. I am still confused though :/ I don't understand the last equality; ##\langle \frac{\delta l}{\delta u} , \delta u \rangle = \int \frac{\delta l}{\delta u} \cdot \delta u \hspace{1mm} d V ##. I would think that ## \frac{\delta l}{\delta u} \cdot \delta u ## is the...

Hi, I'm trying to understand the Euler-Poincare equations, which reduce the Euler-Lagrange equations for certain Lagrangians on a Lie group. I'm reading Darryl Holm's "Geometric mechanics and symmetry", where he suddenly uses what seems to be a variational derivative, which I'm having a hard...

thanks a LOT for your answers. I wasn´t sure if it is "bad habit" to bump the thread by saying thank you, so I didn´t. Anyway, I am now almost through the first 5 chapters, and everything has been completely fine withouth knowledge of EM, as you said it would be. I have decided to take part 2...

Great, I understand it now. Thanks a lot!

Hi, I know that I need to find the coefficients, but not how to do it. It becomes an equation with three unknowns? How do i read off the value? I know how to solve this type of problem typically. When the derivative in question is simply the coefficient to x^n times the nth factorial. But...

Hi, I would really appreciate it if someone can help me with the following problem, regarding a taylor polynomial: A 2nd degree taylor polynomial to the function f around x = 1, is given by: T_2(x) = x + x^2 Question: What is f´(1) ? Answer: 3 (Btw: the question is from a multiple...