By Bernard Etkin
The equations of movement obtain a really complete remedy, together with the consequences of the curvature and rotation of the Earth and distortional movement. whole chapters are given to human pilots and dealing with traits and to flight in turbulence, with numerical examples for a jet delivery. Small-perturbation equations for longitudinal and lateral movement look in handy matrix kinds, either in time-domain and Laplace transforms, dimensional and nondimensional.
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2b is the combined block diagram of the subsystems, showing the sort of interconnections and feedbacks that are typically encountered in real systems. Fra. 2 Block diagram. (a)Complete system. ( b ) Detailed block diagram. si = spring forces. d = damper force. ri = reaction forces. 46 Dynamics of atmospheric flight LINEARITY AND TIME INVARIANCE A system is linear if its governing equations are linear in the state variables. I n that case the time functions giving the state variables are simply proportional to the magnitude of nonautonomous input functions of given shape when the initial conditions are zero, and to the initial conditions if there are no nonautonomous inputs.
EQUILIBRIUM, CONTROL, A N D STABILITY Equilibrium denotes a steady state of the system, one in which all the state variables are constant in time. The "motion" corresponding to equilibrium is represented by a point in the state space. The nonautonomous inputs associated with equilibrium must be zero or constant, the zero case preferably corresponding to the equilibrium point at the origin. e. of exercising control over the system is by means of the nonautonomous inputs, the appropriate subset of which can hence be termed the control vector, and the associated space the control space.
It should be pointed out that although there is a minimum number of coordinates (state variables xi and vi) required to specify the state of the system, eight in this example, this number may be arbitrarily increased by redundant variables if it is convenient to do so. For example, we might add the transducer output, the four accelerations ai = d,, and the forces in the springs, even though they are, by virtue of the physical laws governing the system, not independent of the x, and v,. ) The minimum number of state variables required is the order of the system.