# datetime derivations

1. datetime from start/stop

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(t\) | datetime (mid point) | \(s\) since 2000-01-01 | datetime {:}
   \(t_{e}\) | datetime stop | \(s\) since 2000-01-01 | datetime_stop {:}
   \(t_{s}\) | datetime start | \(s\) since 2000-01-01 | datetime_start {:}

   The pattern : for the dimensions can represent {time}, or no dimension at all.

   \[t = \frac{t_{s} + t_{e}}{2}\]

2. datetime from range

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(t\) | datetime (mid point) | \(s\) since 2000-01-01 | datetime {:}
   \(t^{B}(l)\) | datetime boundaries (\(l \in \{1,2\}\)) | \(s\) since 2000-01-01 | datetime_bounds {:,2}

   The pattern : for the dimensions can represent {time}, or no dimension at all.

   \[t = \frac{t^{B}(1) + t^{B}(2)}{2}\]