Celestial mechanics with symplectic integrators

[Masklin]

Homework Statement

The problem is that I just don't understand how the algorithm described here in section 2 hangs together... I have to present this on Thursday morning and that sensation of 'I'll never understand this soon enough' is growing ominously.

Homework Equations

Equations 2,6,7 and 8 are a mystery to me. I could write them out here but they're already in the paper and without their context it wouldn't help much I think.

Why is there a sum from 1 to n in equation 2? What is n? It doesn't say...

And, how is q(t) = exp(tau * F) * q(t-tau) a general solution to dq/dt = Fq ?

Shouldn't it be q(t) = q(tau) * exp(Fq) ?

How does one knows in which order to apply the exponential operators in equation 6?

Where does equation 7 fit in with anything introduced previously?

The Attempt at a Solution

My attempt at a solution is asking for help here... I've googled but my questions are far too specific for that to help. =(

Please please help!Masklin

 

[voko]

Equ. 2 is an application of the chain rule and then Equ. 1. n is the number of the degrees of freedom.

 

[Masklin]

Degrees of freedom - what does that mean in this context? The dimensionality of x and p, or the number of bodies? Or something else?

 

[voko]

The dimension of x.