I'd tend to agree with Daniel's suggestions, although I'm the type that likes to duke it out with overzealous government. After all, we're guilty until proven innocent right? At least in their eyes we are.
Public property is just that, public property. If it is not being used by someone else, you have free use to it. You can't sit there all stinkin' day, but you can go there, do your thing, crack out 42 pullups, do your next rotation in the exercise while a kid plays on the swingset or whatever, come back when he's done and crack off another 30, do something else, come back and finish off your last 18... get it?