WHY JOY-STICK IN THE AIR CRAFT?

Imagine car moving in a plane surface. It is moving on a 2-dimensional surface. Hence it can move in two directions(x and y). In other words, the car can have 2 transnational motions. How about rotations? It can only turn left or right on the surface. It has only one rotational freedom. Hence one steering wheel is enough to turn the car.

Imagine an air-craft flying in a 3-dimensional air space. It can have 3 transnational motions (x,y,and z). It can also rotate about all the three x,y and z axes. Hence the air-craft also has three rotational freedom. ( In 3 dimensions only, the number of rotational freedom and the number of transnational freedom equals).

So, an air-craft needs a three steering wheels. Three wheels are not practically possible. Hence the joy-stick was invented. The mechanism of joy-stick is the same as that used in computer games. The stick can move up and down; can move side ways, can rotate. All the three rotational motions can be controlled by one joy-stick. The stick translates the physical motions of the hand into digital mathematics and there by controls the turning of the air-plane. In the same way, in a computer game, a character or an object is controlled by the joy-stick.

The following formula gives the number of rotational motions or steering wheels required in a given number of dimensions.

Number of steering wheels required = 1/2n(n-1)
n - number of dimensions.
putting n=3, for a air-plane
= 1/2*3*(3-1)
=1/2*3*2
=3. So it is.
putting n=2, for a car, we get 1.
say, putting n=1 for a train, we get zero. That means, no steering wheel is required for a train. The train simply follows the track. Track changing is controlled by the Rail-stations.
The formula says, in a four dimensional world six rotational motions are possible.
Thank god. We do not have to encounter four dimensional world.

The earth spins and revolves. The electron spins and orbits. Water molecules rotates. This three dimensional world with three rotational freedom is highly suitable for them and us.

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