Eigenvector Slew - Problem

Problem

Let

be a body fixed reference system for a 3 axis stabilized spacecraft. The initial attitude is given by

One wants to find an axis relative the spacecraft body

and a rotation angle such that after the rotation with the angle one has that

where

are the new target directions.

In vector form this means that

\hat{d}=r_a \cdot \hat{r} + \cos \alpha \cdot ( \hat{a} - r_a \cdot \hat{r})+ \sin \alpha \cdot \hat{r} \times \hat{a}
\hat{e}=r_b \cdot \hat{r} + \cos \alpha \cdot ( \hat{b} - r_b \cdot \hat{r})+ \sin \alpha \cdot \hat{r} \times \hat{b}
\hat{f}=r_c \cdot \hat{r} + \cos \alpha \cdot ( \hat{c} - r_c \cdot \hat{r})+ \sin \alpha \cdot \hat{r} \times \hat{c}.

Read more about this topic:  Eigenvector Slew

Famous quotes containing the word problem:

    “I tell you, sir, the only safeguard of order and discipline in the modern world is a standardized worker with interchangeable parts. That would solve the entire problem of management.”
    —Jean Giraudoux (1882–1944)

    “Will women find themselves in the same position they have always been? Or do we see liberation as solving the conditions of women in our society?... If we continue to shy away from this problem we will not be able to solve it after independence. But if we can say that our first priority is the emancipation of women, we will become free as members of an oppressed community.”
    —Ruth Mompati (b. 1925)

    “The problem is that we attempt to solve the simplest questions cleverly, thereby rendering them unusually complex. One should seek the simple solution.”
    —Anton Pavlovich Chekhov (1860–1904)