you can probably setup some kind of a NOT/OR/AND circuit that when it detects the 2a from the solar panels it runs the machine straight from them.. with just a trickle charge going to the battery..
then when the sun goes down and the panels dont produce 2a, it will switch to the battery.
That's a good idea, I'll look into that, thanks.
you would have to double check, as im not an expert, but i think something as simple as this would work..
basically the 5v from the top would be your solar panel.. and the input would be your battery..
the 0v is ground and should be common to the whole thing.
you would then also take the 5v from the solar panel and wire it into the battery charging port on the battery as well.. might want to use a couple diodes for that.
when the panel doesnt make 5v, it will get the power from the battery.
hmm, edit looking at this it might not work as this may drain the battery straight to ground.. you might want to put a diode in the 0v line so it doesnt do that.
double edit. i bet you can take apart one of those lights they use for gardens that have the eye in them that senses when it gets dark and turns on and off and use that circuit between the battery and the pi. they only cost like 5$ and have a battery and a small solar panel in them you can use too.
http://www.homedepot.com/p/UNBRANDED-Solar-Black-Spot-Light-S8178/205401446?N=5yc1vZ1z0z3pd