# What is the use of quaternion?

## What is the use of quaternion?

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis.

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### How did Hamilton discover quaternions?

On October 16, 1843, Hamilton and his wife took a walk along the Royal Canal in Dublin. While they walked across Brougham Bridge (now Broom Bridge), a solution suddenly occurred to him. While he could not “multiply triples”, he saw a way to do so for quadruples.

#### What is quaternion theory?

Quaternions were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors.

What are four quaternions?

quaternion. / (kwəˈtɜːnɪən) / noun. maths a generalized complex number consisting of four components, x = x 0 + x 1 i + x 2 j + x 3 k, where x, x 0 … x 3 are real numbers and i² = j² = k² = –1, ij = –ji = k, etc.

How do you calculate quaternions?

💡 Quaternions are expressions of the form q = a + b*i + c*j + d*k , where a , b , c , and d are arbitrary real numbers and i , j , and k are base elements sometimes called the basic unity quaternions.

## How do you calculate quaternion?

### What is a quaternion in the Bible?

a group or set of four persons or things. Bookbinding. four gathered sheets folded in two for binding together. Mathematics.

#### What is Hamilton quaternion?

Hamilton defined a quaternion as the quotient of two directed lines in tridimensional space; or, more generally, as the quotient of two vectors. A quaternion can be represented as the sum of a scalar and a vector. It can also be represented as the product of its tensor and its versor.

Are quaternions 4D?

The quaternions are a four dimensional vectorspace over the reals. However, being a “4D vector” is more than just having four components. Being part of a vectorspaces says something about how you can interact with other things.

How many quaternions are there?

a group or set of four persons or things.

## How to think about quaternions?

Quaternions and 3d rotation. One of the main practical uses of quaternions is in how they describe 3d-rotation.

• Stereographic projection. One thing that makes quaternions so challenging is that they live and act in four dimensions,which is extremely hard (impossible?) to visualize.
• Quaternion multiplication.
• Credits and thanks.
• ### Why should quaternions exist?

Avoiding gimbal lock,a problem with systems such as Euler angles.

• Faster and more compact than matrices.
• Nonsingular representation (compared with Euler angles for example).
• Pairs of unit quaternions represent a rotation in 4D space (see Rotations in 4 dimensional Euclidean space: Algebra of 4D rotations ).
• #### How to combine quaternions?

Constraining any two of b,c and d to zero produces a representation of complex numbers.

• 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.
• How are quaternions applicable in physics?

– Introduction. Quaternions have found a permanent place in engineering and computer description of moving objects. – Electromechanics. – Quantum mechanics. – 3D animation. – Topology. – See also.