NAVWEPS 00-802-80  STABILITY ,AND CONTROL  DYNAMIC STABILITY  245  to zero. When an aircraft is in equilibrium,  there are no accelerations and the aircraft  continues in a steady condition of flight.  If  the equilibrium is disturbed by a gust or deflec-  tion of the controls, the aircraft will experi-  ence acceleration due to unbalance of moment  or force.  The static stability of a system is defined by  the initial tendency to return to equilibrium  conditions following some disturbance from  equilibrium.  If an object is disturbed from  equilibrium and has the tendency to return  to equilibrium, positive .rtatic Jtability exists.  If the object has a tendency to continue in the  direction of disturbance, negative  static stability  or static instability exists. An intermediate  condition could occur where an object dis-  placed from equilibrium remains in equilibrium  in the displaced position.  If the object subject  to a disturbance has neither the tendency to  return nor the tendency to continue in the dis-  placement direction, ncutrnl Jtatic stability ex-  ists. These three categories of static stability  are illustrated in figure 4.1.  The ball in a  trough illustrates the condition of positive  static stability.  If the ball is displaced from  equilibrium at the bottom of the trough, the  initial tendency of the ball is to return to the  equilibrium  condition.  The ball may roll  back and forth through the point of equilib-  rium but displacement to either side creates  the initial tendency to return.  The ball on a  hill illustrates the condition of static insta-  bility.  Displacement from equilibrium at the  hilltop brings about the tendency for greater  displacement. The ball on a flat, level surface  illustrates the condition of neutral static sta-  bility.  The ball encounters  a new equilibrium  at any point of displacement and has neither  stable nor unstable tendencies.  The term “static”  is applied to this form of  stability since the resulting motion is not  considered. Only the tendency  to return to  1.  eqmlibrtum conditions is considered in static  stability.  The static longitudinal stability of  an aircraft is appreciated by displacing the  The oscillatory modes of figure 4.2 depict the  time histories possible with cyclic motion.  One feature common to each of these modes is  that positive static stability is demonstrated in  the cyclic motion by tendency to return to  While static stability is concerned with the  tendency of a displaced body to return to  equilibrium,  dynamic stability is defined by  the resulting motion with time.  If an object is  disturbed from equilibrium, the time history  of the resulting motion indicates the dynamic  stability of the system. In general, the system  will  demonstrate positive dynamic stability  if the amplitude of motion decreases  with  time.  The various condirions of possible  dynamic behavior are illustrated by the time  history diagrams of figure 4.2.  The nonoscillatory modes shown in figure  4.2 depict the time histories possible without  cyclic motion.  If the system is given an initial  disturbance and the motion simply subsides  without oscillation, the mode is termed “sub-  sidence” or “deadbeat return.”  Such a motion  indicates positive static stability by the tend-  ency to return to equilibrium and positive dy-  namic stability since the amplitude decreases  with time.  Chart B illustrates the mode of  “divergence” by a noncyclic increase  of ampli-  tude with time. The initial tendency to con-  tinue in the displacement direction is evidence  of static instability and the increasing ampli-  tude is proof of dynamic instability.  Chart C  illustrates the mode of pure neutral stability.  If the original disturbance creates a displace-  ment which remains constant thereafter, the  lack of tendency for motion and the constant  amplitude indicate neutral static and neutral  dynamic stability.  aircraft from some trimmed angle of attack.  If the aerodynamic pitching moments created  by this displacement tend to return the air-  craft to the equilibrium angle of attack the  aircraft  has  positive  static  longitudinal  stability. 