How do you make a Quaternion?

Question

I went onto Wikipedia and searched Quaternion but the result was very confusing. Could someone tell me how to make a Quaternion if you are just a middle-schooler? Thanks!!! By the way, Quaterniions are used to predict the orbit of satellites. When I mean satellites, I mean a celestial body orbiting another celestial body.

Answer 1

Quaternions are an extension of the idea of complex numbers. A general complex number can be written as

a+bi

where i^2=-1 and a and b are real numbers. In the same way, a general quaternion can be written as

a+bi+cj+dk

where i^2=j^2=k^2=ijk=-1.

The quaternions form an 'algebra' which is not commutative: in other words, if z and w are quaternions, it may happen that zw and wz are different! In fact, ij=k, but ji=-k. There are associative, however.

Quaternions were first used to describe rotations, although today we use matrices for this.  This is the main reason they are applicable to satellite orbits.

Answer 2

A 'quaternion' can be thought of as a pair of complex-valued numbers.  But, more generally, it's best to think of it as you would any other ordered n-tuple which represents a point in n-space.  A quaternion is simply the special case of an n-tuple which has 4 elements (and thus locates a point in 4-dimensional space) while a complex number (which has 2 elements) locates points in a 2-dimensional space (a plane).

You'll get into higher-dimensional mathematics soon enough ☺

HTH,

Doug

Answer 3

A quaternion is a math number thing. Not a predicting satellite thing. Even if it were a satellite predicter, i doubt a high schooler let alone middle schooler could make it