Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I have the following function:

[itex]\textbf{h}[/itex]([itex]\textbf{x}[/itex]) = [ [itex]\textbf{C}[/itex][itex]^{n}_{b2}[/itex] ][itex]^{T}[/itex] [itex]\textbf{C}[/itex][itex]^{n}_{b1}[/itex] [itex]\textbf{C}[/itex][itex]^{b1}_{b2}[/itex]

with

[itex]\textbf{x}[/itex] = [ [itex]\textbf{ε}[/itex][itex]_{1}[/itex][itex]\;[/itex] [itex]\textbf{ε}[/itex][itex]_{2}[/itex] ][itex]^{T}[/itex] containing Euler angles [itex]\mathbf{ε}[/itex] such that direction cosine matrix [itex]\textbf{C}[/itex][itex]^{n}_{b1}[/itex] is a function of [itex]\textbf{ε}[/itex][itex]_{1}[/itex] and [itex]\textbf{C}[/itex][itex]^{n}_{b2}[/itex] is a function of [itex]\textbf{ε}[/itex][itex]_{2}[/itex] (through the relationship linking Euler angles and their corresponding cosine matrix), and [itex] b1, b2, n [/itex] are different reference frames.

I want to linearize [itex]\textbf{h}[/itex]([itex]\textbf{x}[/itex]) with respect to [itex]\textbf{ε}[/itex][itex]_{1}[/itex] and [itex]\textbf{ε}[/itex][itex]_{2}[/itex], which should give me the following (3 x 6) matrix:

[itex] \mathbf{H} = \left[ \frac{\partial \textbf{h}(\textbf{x})}{\partial \textbf{ε}_{1}} \frac{\partial \textbf{h}(\textbf{x})}{\partial \textbf{ε}_{2}} \right][/itex]

Could anyone give me hints on how I could solve this problem,i.e.compute the elements of [itex]\mathbf{H}[/itex]? Thank you in advance for your suggestions

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Linearization of product of rotation matrices

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Linearization product rotation | Date |
---|---|

What is the largest number of mutually obtuse vectors in Rn? | Jan 28, 2016 |

Question about Cyclical Matrices and Coplanarity of Vectors | Sep 3, 2015 |

Linear Algebra; Transformation of cross product | May 19, 2015 |

Non-square linear systems with exterior product | Sep 11, 2014 |

Normed linear space vs inner product space and more | Oct 15, 2013 |

**Physics Forums - The Fusion of Science and Community**