This this Wikipedia page states that symplecticness (being symplectic) is a property of particle systems governed by Hamilton's equation. I am thinking of classical-mechanics point particles described by position and momentum, nothing particularly 'fancy'.
I can see how Hamilton's equations can govern the evolution of a system of particles. However, I lack an understanding of the physical meaningfulness of symplecticness as a descriptive property, and of what could go paradoxical if this property is not respected.
The resources I found along the way lean to the side of mathematical formalism [1-4]. After curiosity I looked for the etymology of the word; although I found no authoritative source, the word symplectic could have to do with 'hitting together', so matters involving friction or being complementary.
Would someone please provide some explanation and examples to show why symplecticness is important for describing the evolution of particle systems?
From this community, but still too jargonistic for me: