Suppose we have these sentences:
1. Smiling, she offered me a hot cup of chocolate. 2. Busy finishing my homework, I have no time to even think about video games. 3. Knowing there's little change of being selected, Tim did not try out for the team. 4. Having visited NYC, now I know what real cities are like 5. Happily, he took my advice.
In the 5 sentences above, we have gerunds (
"knowing there's little change of being selected"), adjective (
"busy finishing my homework"), verb participle form (
"having visited NYC"), and adjective (
"happily") all describing a certain state of being of the subject.
What is the formal name for such a grammatical element/structure?