I wouldn't worry too much about getting into the DEs side of things unless you fancy a touch of math brain strain.
A characteristic of rotating machinery (of which all our engines, piston, jet, turboprop are examples) is a phenomenon referred to as whirling or whirl mode which is a resonance thing where the shaft does interesting gyrations and can suffer severe structural distress. While the combinations of different machinery assemblies complicate the issue, the basic phenomenon occurs with something as simple as a spinning rod.
Suggest you do a Google (or whatever search engine turns you on) for "whirl modes" and sift amongst the hits. I ran a Google search and turned up near 200 hits including helo and fixed wing references ...
Happy reading ...