Share this document with a friend

Description:

Popular Tags:

29

Quaternion Arithmetic Elmer Nocon Angelo Bernabe Mark Hitosis

Transcript

- 1. Quaternion Arithmetic

Elmer Nocon

Angelo Bernabe

Mark Hitosis

2. Quaternion Addition

Let

and

be two quaternions.

the sum of P and Q is

3. Quaternion Addition

Let

and

be two quaternions.

the sum of P and Q is

4. Quaternion Addition

Let

and

be two quaternions.

the sum of P and Q is

e5

5. Quaternion Addition

Let

and

be two quaternions.

the sum of P and Q is

6. Quaternion Addition

Let

and

be two quaternions.

the sum of P and Q is

e

7. Quaternion Addition

Example:

Let

and

be two quaternions.

the sum of S and T is

8. Quaternion Subtraction

Let

and

be two quaternions.

the difference of P and Q is

9. Quaternion Subtraction

Let

and

be two quaternions.

the difference of P and Q is

10. Quaternion Subtraction

Let

and

be two quaternions.

the difference of P and Q is

11. Quaternion Subtraction

Let

and

be two quaternions.

the difference of P and Q is

12. Quaternion Subtraction

Let

and

be two quaternions.

the difference of P and Q is

13. Quaternion Subtraction

Example:

Let

and

be two quaternions.

the difference of S and T is

14. Quaternion Multiplication

Let

and

be two quaternions.

the product of P and Q is

15. Quaternion Multiplication

Let

and

be two quaternions.

the product of P and Q is

we distribute

16. When we multiply the imaginary operators we use the following
rules:

17. When we multiply the imaginary operators we use the following
rules:

18. When we multiply the imaginary operators we use the following
rules:

19. then we simplify

our newly derived formula

20. Quaternion Multiplication

Example:

Let

and

be two quaternions.

the product of S and T is

using our formula

21. Quaternion Division

Let

and

be two quaternions.

to find the quotient of P and Q

we need to multiply P by the reciprocal of Q

and to find the Q-1,

we need to find the conjugate of q and divide it by the normal of
q

22. Quaternion Conjugation

Let

be a quaternion.

the conjugate of P is

23. Quaternion Conjugation

Example:

Let

be a quaternion.

the conjugate of P is

24. Normal of a Quaternion

Let

be a quaternion.

the normal of P is

25. Normal of a Quaternion

Example:

Let

be a quaternion.

the normal of P is

26. Reciprocal of a Quaternion

Let

be a quaternion.

the reciprocal of P is

27. Reciprocal of a Quaternion

Example:

Let

be a quaternion.

the reciprocal of P is

28. Quaternion Division

Example:

Let

and

be two quaternions.

the quotient of P and Q is

29. Quaternion Division

we use our formula in quaternion multiplication

Recommended