# datetime start derivations

1. datetime start from datetime and stop

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(t\) | datetime (mid point) | \(s\) since 2000-01-01 | datetime {:}
   \(t_{s}\) | datetime start | \(s\) since 2000-01-01 | datetime_start {:}
   \(\Delta t\) | time duration | \(s\) | datetime_length {:}

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

   \[t_{s} = t - \frac{\Delta t}{2}\]

2. datetime start from range

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

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

   \[t_{s} = t^{B}(1)\]