BUG: Fix no time initialization when passing initial_solution as array to Flight object (#844)

## Pull request type

- [x] Code changes (bugfix, features)
- [x] Code maintenance (refactoring, formatting, tests)

## Checklist

- [ ] Tests for the changes have been added (if needed)
- [ ] Docs have been reviewed and added / updated
- [ ] Lint (`black rocketpy/ tests/`) has passed locally
- [ ] All tests (`pytest tests -m slow --runslow`) have passed locally
- [ ] `CHANGELOG.md` has been updated (if relevant)

## Current behavior
Passing initial_solution to a Flight object raises `AttributeError: 'Flight' object has no attribute 't_initial'` when running a simulation involving a controller. Attempt to run [this script](https://github.com/werocketry/airbrakes-lookuptable-generator/blob/main/main.py) to reproduce.

## New behavior
Initializes t_initial in __init_flight_state when an array is provided as the initial solution. As a result, a simulation can successfully run from an initial condition when controllers are used.

Additionally, minor fixes to docstrings in Flight.py

## Breaking change

- [ ] Yes
- [x] No

Author: chasgior214

rocketpy/simulation/flight.py

@@ -143,7 +143,7 @@ class Flight:
     Flight.heading : int, float
         Launch heading angle relative to north given in degrees.
     Flight.initial_solution : list
-        List defines initial condition - [tInit, x_init,
+        List defines initial condition - [t_initial, x_init,
         y_init, z_init, vx_init, vy_init, vz_init, e0_init, e1_init,
         e2_init, e3_init, w1_init, w2_init, w3_init]
     Flight.t_initial : int, float
@@ -155,10 +155,6 @@ class Flight:
         Current integration time.
     Flight.y : list
         Current integration state vector u.
-    Flight.initial_solution : list
-        List defines initial condition - [tInit, x_init,
-        y_init, z_init, vx_init, vy_init, vz_init, e0_init, e1_init,
-        e2_init, e3_init, w1_init, w2_init, w3_init]
     Flight.out_of_rail_time : int, float
         Time, in seconds, in which the rocket completely leaves the
         rail.
@@ -544,7 +540,7 @@ def __init__(  # pylint: disable=too-many-arguments,too-many-statements
         rtol : float, array, optional
             Maximum relative error tolerance to be tolerated in the
             integration scheme. Can be given as array for each
-            state space variable. Default is 1e-3.
+            state space variable. Default is 1e-6.
         atol : float, optional
             Maximum absolute error tolerance to be tolerated in the
             integration scheme. Can be given as array for each
@@ -1168,6 +1164,7 @@ def __init_flight_state(self):
             self.out_of_rail_state = self.initial_solution[1:]
             self.out_of_rail_time = self.initial_solution[0]
             self.out_of_rail_time_index = 0
+            self.t_initial = self.initial_solution[0]
             self.initial_derivative = self.u_dot_generalized
         if self._controllers or self.sensors:
             # Handle post process during simulation, get initial accel/forces
@@ -2080,7 +2077,7 @@ def x(self):
 
     @funcify_method("Time (s)", "Y (m)", "spline", "constant")
     def y(self):
-        """Rocket y position relative to the lauch pad as a Function of
+        """Rocket y position relative to the launch pad as a Function of
         time."""
         return self.solution_array[:, [0, 2]]
 
@@ -2976,7 +2973,7 @@ def max_rail_button2_shear_force(self):
         "Time (s)", "Horizontal Distance to Launch Point (m)", "spline", "constant"
     )
     def drift(self):
-        """Rocket horizontal distance to tha launch point, in meters, as a
+        """Rocket horizontal distance to the launch point, in meters, as a
         Function of time."""
         return np.column_stack(
             (self.time, (self.x[:, 1] ** 2 + self.y[:, 1] ** 2) ** 0.5)