How do you make a Quaternion?
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.
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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.
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 âº
HTH,
Doug
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