This is the steady-state component of a system response, ie once all dynamic behaviour has decayed, and is essentially the gain between the inputs and outputs. In a physical sense this is determined by things like actuator sizing, motor coefficients and thermal transfer coefficients.

Statics is the branch of mechanics concerned with the analysis of loads (force, torque/moment) on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity. When in static equilibrium, the system is either at rest, or its center of mass moves at constant velocity. The study of moving bodies is known as dynamics, and in fact the entire field of statics is a special case of dynamics.

By Newton's first law, this situation implies that the net force and net torque (also known as moment of force) on every body in the system is zero. From this constraint, such quantities as stress or pressure can be derived. The net forces equalling zero is known as the first condition for equilibrium, and the net torque equalling zero is known as the second condition for equilibrium. See statically determinate.

Solids
Statics is used in the analysis of structures, for instance in architectural and structural engineering. Strength of materials is a related field of mechanics that relies heavily on the application of static equilibrium. A key concept is the center of gravity of a body at rest: it represents an imaginary point at which all the mass of a body resides. The position of the point relative to the foundations on which a body lies determines its stability towards small movements. If the center of gravity exists outside the foundations, then the body is unstable because there is a torque acting: any small disturbance will cause the body to fall or topple. If the center of gravity exists within the foundations, the body is stable since no net torque acts on the body. If the center of gravity coincides with the foundations, then the body is said to be metastable.

Fluids
Hydrostatics, also known as fluid statics, is the study of fluids at rest. This analyzes bodies of fluid in static equilibrium. The characteristic of any fluid at rest is that the force exerted on any particle of the fluid is the same at all points at the same depth (or altitude) within the fluid. If the net force is greater than zero the fluid will move in the direction of the resulting force. This concept was first formulated in a slightly extended form by the French mathematician and philosopher Blaise Pascal in 1647 and would be later known as Pascal's Law. This law has many important applications in hydraulics. Archimedes, Abū Rayhān al-Bīrūnī, Al-Khazini[2] and Galileo Galilei were also major figures in the development of hydrostatics. Read more!