aero- + -dyne (clipped from the base of Greek dýnasthai "to have the capacity (to), be capable of," dýnamis "power") — more at dynamic entry 1
The clipping of dynam- to a single syllable is presumably to put it in line with the similar monosyllabic terminations of other terms beginning with aero- and associated with artificial flight, such as aerostat and aeroplane. The term was apparently coined by the Canadian engineer Wallace Rupert Trumbull (1870-1954), and was introduced in a letter to Scientific American (vol. 95, no. 12, September 22, 1906, p. 211): "Properly speaking an airplane can only be one of the parts, and not the whole, of an aeronef; for aeroplanes are used in kites, in soaring machines, and in aerodynes, which is the term I wish to propose to denote aeroplane-supported machines, driven by mechanical power (i.e., by a prime mover). The Greek roots of aerodyne are obvious…The word aerodyne should be capable of international acceptance, and I would therefore suggest that in future the subdivisions of aeronef be: helicopter, orthopter, soaring machine, and aerodyne…. W. R. Trumbull, Rothesay, N.B., Canada, September 8, 1906 [italics as in original]."