Here's what rhymes with gyrostatic.
static hepatic prostatic somatic thematic ecstatic erratic asthmatic fanatic operatic spermatic dramatic automatic dogmatic emphatic schematic traumatic hydrostatic lymphatic pneumatic rheumatic chromatic prismatic orthostatic stigmatic photostatic aerobatic systematic aromatic climatic pragmatic autocratic charismatic enzymatic metastatic aliphatic cinematic psychosomatic achromatic homeostatic idiomatic magmatic muriatic phlegmatic theocratic zygomatic acrobatic schismatic astigmatic thermostatic democratic diplomatic aristocratic bureaucratic pancreatic symptomatic electrostatic enigmatic axiomatic emblematic kinematic diagrammatic diaphragmatic intrahepatic posttraumatic numismatic panchromatic undramatic unemphatic homoeostatic problematic asymptomatic paradigmatic programmatic technocratic unsystematic epigrammatic plutocratic semiautomatic nondramatic unidiomatic idiosyncratic melodramatic monochromatic undemocratic antidemocratic meritocratic undiplomatic unproblematic nondemocratic Words that almost rhyme with gyrostatic
magic tragic sporadic pelagic syllabic apparatchik priapic nomadic disyllabic polysyllabic monosyllabic panic tactic spastic tannic traffic plastic ceramic drastic frantic lactic manic oceanic synaptic phallic italic satanic mastic tyrannic dynamic organic classic elastic romantic fabric fantastic gastric gigantic graphic metallic semantic thoracic catholic didactic dynastic stochastic cephalic nostalgic pedantic thalamic aplastic clastic titanic isobaric slapstick ataxic botanic malefic baldric psychiatric monastic scholastic volcanic barbaric hemorrhagic mechanic pediatric sarcastic galactic geriatric glutamic messianic ophthalmic panoramic postsynaptic presynaptic tympanic gymnastic haemorrhagic heraldic psychopathic splanchnic bimetallic bombastic chiropractic orgiastic paediatric matchstick geographic inorganic photographic hypothalamic inelastic neoplastic prophylactic aerodynamic climactic ecclesiastic galvanic telegraphic hyperplastic hypoplastic lithographic orthographic thermoplastic tomographic typographic unromantic biographic neoclassic osteopathic periphrastic sycophantic demographic enthusiastic cytoplasmic ethnographic thermodynamic hemodynamic hydrodynamic pornographic psychodynamic topographic transatlantic anaphylactic holographic protoplasmic viscoelastic nonmetallic oceanographic stenographic calligraphic transoceanic phonographic xerographic nonelastic radiographic bibliographic chromatographic endoplasmic stratigraphic angiographic cartographic iconoclastic iconographic intrathoracic choreographic intergalactic seismographic crystallographic unenthusiastic anticlimactic autobiographic interscholastic lexicographic overenthusiastic cinematographic electrocardiographic electroencephalographic