Great topic, Dr. A.
This is my biological puzzle.
Most insects mate by coupling the genitalia at the terminal segments of of the abdomen.
Odonate mating is much more complicated. Both sexes still have genital openings at the end of the abdomen, but the male also has accessory genitalia on the second abdominal segment.
The male transfers sperm packets to the accessory genitalia prior to mating. He also has appendages at the end of the abdomen that are used to grasp the head of the female (in dragonflies) or the pro-thorax or meso-thorax of the female (in damselflies). Now these male appendages are unique to each species and can be quite intricate with lumps, depressions, spines, hairs, etc. and the fit quite specifically with the female, kind of like a lock and key, but also stimulating sensory regions.
Occasionally, males of another species will attempt to mate with a female by grasping her head but she will not copulate unless she senses a male of her own species.
Once the male is coupled with the female, she will swing her abdomen forward until the tip contacts the male's accessory genitalia. Here we have more intricate apparatus, that not only transfers sperm to a special organ in the female, but may also scoop out or pack down (depending on species) any sperm already there from prior matings with competing males. This copulation may be very brief (a few seconds) to many hours, again depending on species. Most species can fly around quite well in this
wheel position and it may be a common sight around aquatic habitats in the Summer.
The male may remain attached to the female while she oviposits or he may guard her to keep other males from mating.
I have spent most of my life studying dragonflies and their mating. It is extremely complex, not just in morphology but also in behavior. There is a fairly large community of scientists who study Odonates and none of us has offered what I consider a really satisfying explanation of how their mating morphology and behavior evolved.
What if Eleanor Roosevelt had wings? -- Monty Python
You can't build a Time Machine without Weird Optics -- S. Valley