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Calculate product of two quaternions

**Library:**Aerospace Blockset / Utilities / Math Operations

The Quaternion Multiplication block calculates the product for two given quaternions. For more information on the quaternion forms, see Algorithms.

This block uses quaternions of the form of

$$q={q}_{0}+i{q}_{1}+j{q}_{2}+k{q}_{3}$$

and

$$r={r}_{0}+i{r}_{1}+j{r}_{2}+k{r}_{3}.$$

The quaternion product has the form of

$$t=q\times r={t}_{0}+i{t}_{1}+j{t}_{2}+k{t}_{3},$$

where

$$\begin{array}{l}{t}_{0}=({r}_{0}{q}_{0}-{r}_{1}{q}_{1}-{r}_{2}{q}_{2}-{r}_{3}{q}_{3})\\ {t}_{1}=({r}_{0}{q}_{1}+{r}_{1}{q}_{0}-{r}_{2}{q}_{3}+{r}_{3}{q}_{2})\\ {t}_{2}=({r}_{0}{q}_{2}+{r}_{1}{q}_{3}+{r}_{2}{q}_{0}-{r}_{3}{q}_{1})\\ {t}_{3}=({r}_{0}{q}_{3}-{r}_{1}{q}_{2}+{r}_{2}{q}_{1}+{r}_{3}{q}_{0})\end{array}$$

[1] Stevens, Brian L., Frank L. Lewis,
*Aircraft Control and Simulation*, 2nd edition Hoboken, NJ:
John Wiley & Sons, 2003.

Quaternion Conjugate | Quaternion Division | Quaternion Inverse | Quaternion Modulus | Quaternion Norm | Quaternion Normalize | Quaternion Rotation