What are quaternions used for in physics?

Physics: The quaternions have found use in a wide variety of research. – They can be used to express the Lorentz Transform making them useful for work on Special and General Relativity[9].

Are quaternions useful for implementing?

Quaternions are used in computer graphics when a 3D character rotation is involved. Quaternions allows a character to rotate about multiple axis simultaneously instead of sequentially, as matrix rotation allows. Quaternions consume less memory and are faster to compute than matrices.

What does a quaternion represent?

A quaternion represents two things. It has an x, y, and z component, which represents the axis about which a rotation will occur. It also has a w component, which represents the amount of rotation which will occur about this axis. In short, a vector, and a float.

Why do quaternions represent rotation?

Quaternions are very efficient for analyzing situations where rotations in R3 are involved. A quaternion is a 4-tuple, which is a more concise representation than a rotation matrix. Its geo- metric meaning is also more obvious as the rotation axis and angle can be trivially recovered.

What are Octonions used for?

Octonions are an 8-dimensional analog of complex numbers, and can be used to represent arbitrary rotations in 7 dimensions. In general, they aren’t used much, but sometimes they show up as potentially useful tools. You can build up to octonions the following way: Real numbers are the numbers we are used to.

What is the norm of a quaternion?

The norm of a quaternion (the square root of the product with its conjugate, as with complex numbers) is the square root of the determinant of the corresponding matrix. The conjugate of a quaternion corresponds to the conjugate transpose of the matrix.

Why are quaternions better?

Because they have a number of appealing properties. First one can nicely interpolate them, which is important if one is animating rotating things, like the limbs around a joint. With a quaternion it is just scalar multiplication and normalization.

Are octonions Clifford algebra?

but the octonions are not a Clifford algebra, since they are nonassociative. Nonetheless, there is a profound relation between Clifford algebras and normed division algebras. This relationship gives a nice way to prove that $\R,\C,\H$ and $\O$ are the only normed dvivision algebras.