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dynam motion missil descend atmospher method present comput rapidli yet accur dynam motion ballist type missil descend atmospher equat motion separ set static trajectori equat zero angl attack set rotat equat describ oscillatori motion missil center graviti transform allow rotat equat written manner analog equat undamp oscil spring mass system mass equal uniti time variabl spring constant given initi condit equat solv obtain envelop maximum angl attack addit transform allow calcul complet oscillatori motion time trajectori function maximum angl attack time solut show maximum angl attack missil descend atmospher rel constant speed reduc even aerodynam damp neglect