/sci/ - Science & Math

Squares of [math]\mathbf{i}[/math], [math]\mathbf{j}[/math], [math]\mathbf{k}[/math]
The product [math]\mathbf{ijk}[/math], and
Minus one: the same!

Why don't we use quaternions in contemporary mathematics as much as we used to? One can mathematically deduce the dot and cross products of vectors by interpreting vectors in terms of quaternions, as purely imaginary quaternions, and any purely imaginary quaternion with a norm of one can be a square root of -1. William Rowan Hamilton, the most influential mathematician of the 19th century, devoted most of his studies developing the theory of quaternions and applying it in mathematical physics, and James Clerk Maxwell derived his work in terms of quaternions. Yet we don't even hear of quaternions in school.

Anyone have a good resource for Quaternion manipulation, i only have a general application based understanding

Sir William Rowan Hamilton seems to have been a pretty cool guy.
He's an example of a child prodigy who managed to become successful.

Starting from the principle of extreme action (usually called "least" action, but technically it's just stationary), we can derive the laws of motion. It's mathematically appealing and it works, but what justifies starting with this principle?

Is it axiomatic and empirical or is there something that justifies it?

Most texts start with "ok, let's say that there is something called the action, and that it is minimized between two points in coordinate space". I just want to understand how you can start with that in the first place.

Any freely accessible resources explaining the physical meaning of the action in an intuitive way would be greatly appreciated.

>not using quaternions
I seriously hope you just still don't do this