# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Message:αβγ
Message:abc
 Add Images & Files Posting Code: Name: Email:
Re: Spacecraft Attitude Determination and Control
From: Dan Allen
Date: 2003 Feb 13, 19:20 -0800

```On Thursday, February 13, 2003, at 05:20 PM, Robert Eno wrote:

> What is a quaternion?

In the world of mathematics there are a variety of numbers:

* scalars
- single numbers (3.14, 58)
* complex numbers
- pairs of numbers like x,y points (1,2)
- also written as real + imaginary (1+2i)
- a set of arithmetic operations are defined such that
the square root of -1 is an imaginary number called i
* vectors
- several numbers (often 2-4) grouped together (1,2,3)
- often used to represent dimensions of space and time
- special operations like dot and cross product defined
- used in navigation, i.e., a 2D vector is distance & course
* tensors
- a matrix of numbers used in advanced physics & relativity
[(1,2,3)(4,5,6)]
- a generalization of vectors
* quaternions
- 4 numbers grouped together (q1,q2,q3,q4)
- used in rigid body rotations and computer graphics
- invented by Sir William Rowan Hamilton, circa 1866.
- allows multiple rotations be to computed with fewer operations
- think of them as a cross between a 3D vector and a complex number
- shares some properties of both vectors and complex numbers

http://www.cs.berkeley.edu/~laura/cs184/quat/quaternion.html for more.

Dan

```
Browse Files

Drop Files

### Join NavList

 Name: (please, no nicknames or handles) Email:
 Do you want to receive all group messages by email? Yes No
You can also join by posting. Your first on-topic post automatically makes you a member.

### Posting Code

Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.
 Email:

### Email Settings

 Posting Code:

### Custom Index

 Subject: Author: Start date: (yyyymm dd) End date: (yyyymm dd)