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.

Comments

Your heart -you do not know

Size and Location: The human heart is roughly the size of a clenched fist and is located slightly to the left of the center of the chest. Despite its relatively small size, the heart plays a crucial role in pumping blood throughout the entire body. Heartbeat Variability: The heart does not beat at a constant rate. The interval between heartbeats can vary, and this variability is considered a sign of a healthy heart. Factors such as breathing, emotions, and physical activity influence the heartbeat. Electrical Conduction: The heart's contractions are controlled by electrical impulses. The sinoatrial (SA) node, often called the "natural pacemaker," generates electrical signals that regulate the heartbeat and coordinate the pumping of blood. Blood Pumping Capacity: On average, the human heart pumps about 2,000 gallons (or 7,570 liters) of blood each day. Over a lifetime, this amounts to pumping enough blood to fill several Olympic-sized swimming pools. Heart Chambers and V...

THE WORK HORSE "="

One cannot think of a mathematical step without 'is equal to ' . It balances right hand side and left hand side. It aids simplification and manipulation of a mathematical expression. example: 2(A+B) = C 2A+2B = C 2A = C-2B A = C-2B/ 2 In an electronic calculator, the pressing of ' = " sign executes an asthmatic expression or simply calculates. In computer languages, it plays very important role. A = B When a computer looks at this expression, the value stored in the location named B is just transferred to the storage named A . After execution both A and B will have the same value an...

How does your smart phone detect motion, steps, rotation, and location?

How it works-1 An accelerometer in a smartphone is a microelectromechanical system (MEMS) device that measures acceleration and tilt. It works by detecting changes in motion by measuring the vibration or acceleration of the device. The accelerometer consists of a small mass suspended on a spring inside a sealed chamber. When the device is subjected to acceleration, the mass moves relative to the device, causing a change in capacitance that can be measured and processed by the smartphone's hardware. The accelerometer measures acceleration in three dimensions (x, y, and z) and provides data that the smartphone's software can use to determine the device's orientation, detect motion, and track changes in velocity and acceleration. The accelerometer is used for a variety of purposes in a smartphone, including screen rotation, motion tracking for games and fitness apps, and detecting the position of the device for navigation and location services. Additionally, it can be used t...

sciencecapsules

Search This Blog