Nomenclature¶

Vector Notation¶

To make the LaTex amsmath rendering easier to read, vectors are denoted in bold instead of in their tradition form.

For example, position vector is written as \(\vec{r}\). In this documentation it will be denoted as \(\mathbf{r}\).

(1)¶\[\vec{r} \equiv \mathbf{r}\]

This is true for all vectors in PyAstronautics.

Define the general relative vector notation as.

(2)¶\[\mathbf{r}_{ij} = \mathbf{r}_j - \mathbf{r}_i\]

For example

\[\mathbf{r}_{12} = \mathbf{r}_2 - \mathbf{r}_1\]

By stacking the position (\(\mathbf{r}\)) and velocity (\(\mathbf{v}\)) vectors there exists a general state vector \(\mathbf{X}\):

(3)¶\[\begin{split}\mathbf{X} = \begin{bmatrix} \mathbf{r} \\ \mathbf{v} \end{bmatrix}\end{split}\]

(4)¶\[\begin{split}\mathbf{X} = \begin{bmatrix} x \\ y \\ z \\ \dot{x} \\ \dot{y} \\ \dot{z} \end{bmatrix}\end{split}\]