Recent content by ryan88

This page (https://shiyuzhao.wordpress.com/2011/06/08/rotation-matrix-angle-axis-angular-velocity/), gives the following relation: \left[R\vec{\omega}\right]_{\times}=R\left[\vec{\omega}\right]_{\times}R^{T} Where: * ##R## is a DCM (Direction Cosine Matrix) * ##\vec{v}## is the angular...

I am performing a Monte Carlo simulation of a weapon system to determine the effect of variations in weapon characterisitics on the accuracy of the weapon. For example, I might vary the muzzle velocity of the weapon and measure the angles between the aim point and the impact point (i.e. miss...

Ah right, now I feel stupid, lol. Thanks for that, Ryan

Have you tried entering 360 - 25.769 = 334.231?

Hi, I am looking to use the definition from WGS84 to calculate Earth's gravitational potential using spherical harmonics, however I am having some difficulty finding the definition of one of the variables. Gravitational potential is given as the following: V = \frac{GM}{r}\left [ 1 +...

Ok, so how do I know whether a quaternion I define is a right of left quaternion? For example, as I said in an earlier post: Is this an example of a right or left quaternion? Thanks, Ryan

As further clarification of my earlier post, please consider the following diagram: http://img171.imageshack.us/img171/2594/vec1a.png This shows the following vector: v=\begin{bmatrix}0\\1\\0\\0\end{bmatrix} If I want to perform a right handed rotation of 90° around the z axis of the...

In this book: http://books.google.co.uk/books?id=GtzzpUN8VEoC&pg=PP1&lpg=PP1&dq= spacecraft +attitude+determination+and+control&source=bl&ots=6Zv_jlYSPf&sig=cDohT-8MSwbNi2IKImeuXX17boI&hl=en&sa=X&ei=BxsIUNCGOYa90QWbxqz_BA&ved=0CFYQ6AEwAw Unfortunately the page in question is not part of the...

If I have a vector like so: v=\begin{bmatrix} 0\\ 1\\ 0\\ 0 \end{bmatrix} and the following quaternion which should perform a 90° rotation about the z axis: v=\begin{bmatrix} 0.7071\\ 0\\ 0\\ 0.7071 \end{bmatrix} I would expect to obtain the following vector...

Hi, I have been looking at quaternions to perform rotations, however I have come across two slightly different equations to do this: v' = q^{-1}vq v' = qvq^{-1} What is the difference between these two? Thanks, Ryan

After taking a closer look at the post I linked to, I have another question. I thought that the time derivative of a rotation matrix was given by: \frac{\mathrm{d}R}{\mathrm{d}t} = \tilde{\omega}R However, in his post, D H states: \mathbf T'_{R\to I} = \mathbf T_{R\to I}\mathbf X(\mathbf...

Ok, after posting this I found the following post in the 'Similar Threads' section at the bottom of the page: https://www.physicsforums.com/showpost.php?p=1650790&postcount=3 It gives a very unambiguous derivation of the equation that I posted earlier.

Hi, I have a couple of questions about velocities in inertial and rotating frames of reference, related by the following equation: \mathbf{v_i} \ \stackrel{\mathrm{def}}{=}\ \frac{d\mathbf{r}}{dt} = \left( \frac{d\mathbf{r}}{dt} \right)_{\mathrm{r}} + \boldsymbol\Omega \times...

Ok, thanks for your help viscousflow. It is very much appreciated. Ryan

Ah yes, I completely missed that. Although substituting \frac{k}{m}=\omega_n^2 leaves the gain of the system as \frac{1}{k} which is then not dimensionless. I thought this transfer function was supposed to be dimensionless?