I admit it. A dangling participle is not what I thought it was. I was confusing it with the grammar rule that is not really a rule, just an accepted practice, a guideline, really, of never ending a sentence with a preposition. I looked it up yesterday.
A dangling participle usually begins with a verb ending in "-ing", then says something about something else. I got this example from wikipedia: "Walking down Main Street, the trees were beautiful." At first glance, it appears that the trees might have been Ents from Fangorn Forest in Middle Earth. Then you realize that there is an unspoken As I was before the walking and I noticed (or saw or observed) before the trees. I found several places that had good articles. I'm especially fond of grammar humor, so this one caught my attention. This one has links and examples and references.
As for the *rule* about never ending a sentence with a preposition: it is a hold-over from Latin, where the modifier always has to be right with whatever it's modifying. I like this article titled "Will I be Arrested if I End a Sentence with a Preposition?" Back when most schools taught Latin, the idea was that proper English should imitate Latin. Obviously Winston Churchill didn't think so. An editor tried to correct a sentence he had ended with a preposition and Churchill had this comment: "This is the sort of English up with which I will not put." Sometimes, that preposition at the end is just what you need to keep your sentence from being laughed at.