position, acceleration is a change in the change

reference system as a nonrotating coordinate

of position. However, before any change can have

frame. It can be either stationary or moving

meaning, it must include the unit of time.

linearly at a uniform speed, in which there are no

Therefore, you can define a change per unit of

inherent forces such as gravity.

time as a rate of change. Thus, a rate of change

You can make a simple test of whether you

of displacement is velocity. A rate of change of

are in a true inertial system by releasing an

velocity is acceleration. A rate of change of a rate

object and observing its motion. If you release

of change of displacement is acceleration.

the object without imparting any acceleration to

it, the object remains in its position relative to

or comparing how one physical property varies

you. If you throw the object, it continues on an

with respect to another. *Integration, *the reverse

undeviating path at a constant speed. Such a

of differentiation, is the process of summing all

system can exist only in empty space, far from

rate of changes that occur within the limits under

any mass, for all masses contain gravitational

investigation.

forces. A reference system attached to the earth

The inertial navigation system is not a

can closely approximate an inertial system. For

differentiating system; it is an integrating system.

this system to work, you must balance the

However, before integration can be done, it must

gravitational force on a body by a second force.

first have a rate of change. Therefore, the

For example, an object sliding on a flat,

inertial navigation system, when stripped to its

frictionless plane on the earth's surface would

barest essentials, is a detector and an integrator.

move in a NEARLY straight line. The object will

It first detects changes of motion. It then

have a NEARLY constant speed, as you saw in

integrates these changes of motion with time to

the earth's coordinate system.

arrive at velocity, and again with time to arrive

at displacement.

because the object will deviate slightly from its

straight-line motion. The cause of this deviation

is the earth's rotation about its axis.

Since an INS performs integration, the follow-

ing is a review of integrating principles.

Newton's second law of motion shares

The equations for the integrals of acceleration

importance with his first law in the inertial

navigation system because the inertial navigation

and velocity are --

system works on Newton's second law. Newton's

second law of motion states *"Acceleration is*

law is written

The physical quality in the above equation that

When acceleration (a) is integrated

over

pertains to the inertial navigation system is

acceleration. You can derive velocity and

a specific period of time (dt), the result is velocity

When velocity (v) is integrated

displacement from acceleration. For example,

over a specific period of time (dt), the result is

consider this fact: Before an object can change

displacement (s). Therefore, when acceleration (a)

its state of rest or state of motion, it must first

is integrated twice

over a specific period of

experience an acceleration. Since acceleration is

time (dt ), the result is displacement (s).

a change in velocity and velocity is a change in

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