ENH: extend flight_rocket to multiple active stages

Fourth slice of the multistage/mission architecture. flight_rocket()
now composes any number of active stages, not just one:
active_stages[0] is the currently firing stage (its motor becomes
the composed Rocket's own motor); every stage above it is inert
cargo, contributing its full current mass/inertia/CoM (structure +
motor + unburned propellant, evaluated at that stage's own t=0)
since its own motor clock hasn't started yet.

Default stack drag (no stack_power_off_drag/on_drag override) is
now an area-weighted sum of each active stage's own drag curve -
the approach mission_multistage_design.md itself leans toward for
_derive_stack_drag. This subsumes the single-stage case from the
previous commit, so that code path is unchanged in behavior.

Split flight_rocket() into _compose_mass_and_center_of_mass and
_compose_inertia to keep it under pylint's statement-count limit,
mirroring how Rocket itself splits mass/inertia composition into
separate evaluate_* methods.

Deviation from the design doc: _stack_position_of() (deriving each
stage's axial position from interstage_lengths + physical extent)
is not implemented. Every active stage's Rocket coordinate system
is assumed to already share one common stack frame; positions are
used as-is. Flagged in the notebook's "Not built yet" section as
remaining work.

Also updates docs/notebooks/multistage_mission.ipynb with a
two-stage (booster + inert sustainer) demo, executed end-to-end
and verified against the same hand-computed values used in
test_multistage.py.

Author: aZira371

docs/notebooks/multistage_mission.ipynb

@@ -11,18 +11,19 @@
     "**Landed so far:**\n",
     "1. `Stage` — wraps a single-stage `Rocket`\n",
     "2. `Deployable` — a carried payload released mid-flight\n",
-    "3. `MultiStageRocket` — composes a stage + its deployables into one flight-ready `Rocket` (single active stage only, for now)\n"
+    "3. `MultiStageRocket` — composes a stage + its deployables into one flight-ready `Rocket`\n",
+    "4. `MultiStageRocket.flight_rocket` for more than one active stage (a booster with an inert sustainer riding on top)\n"
    ]
   },
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@@ -45,10 +46,10 @@
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@@ -101,10 +102,10 @@
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@@ -132,10 +133,10 @@
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-     "shell.execute_reply": "2026-08-14T08:52:34.049445Z"
+     "iopub.execute_input": "2026-08-14T09:07:28.670308Z",
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+     "shell.execute_reply": "2026-08-14T09:07:28.672176Z"
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@@ -158,10 +159,10 @@
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+     "shell.execute_reply": "2026-08-14T09:07:28.676536Z"
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@@ -182,10 +183,10 @@
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+     "shell.execute_reply": "2026-08-14T09:07:28.679876Z"
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@@ -209,10 +210,10 @@
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    "outputs": [],
@@ -245,6 +246,96 @@
     ") < 1e-9"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Multiple active stages: a booster carrying an inert sustainer\n",
+    "\n",
+    "When more than one stage is still attached, `flight_rocket()` treats `active_stages[0]` as the currently firing stage (its motor becomes the composed `Rocket`'s own motor) and every other active stage as inert cargo riding along - contributing its *full* current mass (structure + motor + unburned propellant), since its own motor clock hasn't started yet.\n",
+    "\n",
+    "Each stage's own `Rocket` coordinate system is assumed to already be expressed in a shared stack frame - positions are used as-is. Deriving stack positions automatically from `interstage_lengths` and each stage's physical extent isn't implemented yet."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-08-14T09:07:28.690554Z",
+     "iopub.status.busy": "2026-08-14T09:07:28.690454Z",
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+     "shell.execute_reply": "2026-08-14T09:07:28.708458Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from rocketpy.motors.point_mass_motor import PointMassMotor\n",
+    "\n",
+    "booster_rocket = Rocket(\n",
+    "    radius=0.1,\n",
+    "    mass=10.0,\n",
+    "    inertia=(1.0, 1.0, 0.01),\n",
+    "    power_off_drag=0.5,\n",
+    "    power_on_drag=0.6,\n",
+    "    center_of_mass_without_motor=0.0,\n",
+    ")\n",
+    "booster_rocket.add_motor(\n",
+    "    PointMassMotor(\n",
+    "        thrust_source=100, dry_mass=1.0, propellant_initial_mass=2.0, burn_time=1.0\n",
+    "    ),\n",
+    "    position=0.0,\n",
+    ")\n",
+    "two_stage_booster = Stage(name=\"booster\", rocket=booster_rocket)\n",
+    "\n",
+    "sustainer_rocket = Rocket(\n",
+    "    radius=0.08,\n",
+    "    mass=5.0,\n",
+    "    inertia=(0.5, 0.5, 0.005),\n",
+    "    power_off_drag=0.3,\n",
+    "    power_on_drag=0.4,\n",
+    "    center_of_mass_without_motor=2.0,\n",
+    ")\n",
+    "sustainer_rocket.add_motor(\n",
+    "    PointMassMotor(\n",
+    "        thrust_source=50, dry_mass=0.5, propellant_initial_mass=1.0, burn_time=1.0\n",
+    "    ),\n",
+    "    position=2.0,\n",
+    ")\n",
+    "sustainer = Stage(name=\"sustainer\", rocket=sustainer_rocket)\n",
+    "\n",
+    "two_stage_vehicle = MultiStageRocket(stages=[two_stage_booster, sustainer])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-08-14T09:07:28.710231Z",
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+     "shell.execute_reply": "2026-08-14T09:07:28.725174Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "stacked = two_stage_vehicle.flight_rocket(\n",
+    "    active_stages=(two_stage_booster, sustainer)\n",
+    ")\n",
+    "print(f\"stacked.mass = {stacked.mass} kg  (booster structure + full inert sustainer)\")\n",
+    "print(f\"stacked.center_of_mass_without_motor = {stacked.center_of_mass_without_motor:.4f} m\")\n",
+    "print(f\"stacked.motor is booster_rocket.motor -> {stacked.motor is booster_rocket.motor}\")\n",
+    "\n",
+    "after_separation = two_stage_vehicle.flight_rocket(active_stages=(sustainer,))\n",
+    "print(f\"\\nafter_separation.mass = {after_separation.mass} kg  (sustainer structure only)\")\n",
+    "print(f\"after_separation.motor is sustainer_rocket.motor -> \"\n",
+    "      f\"{after_separation.motor is sustainer_rocket.motor}\")\n",
+    "\n",
+    "assert stacked.mass == 10.0 + (5.0 + 0.5 + 1.0)\n",
+    "assert after_separation.mass == 5.0"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -253,7 +344,7 @@
     "\n",
     "Deliberately out of scope for the commits so far (see the roadmap in `mission_multistage_design.md`):\n",
     "\n",
-    "- `flight_rocket()` for more than one active stage (booster + sustainer composed together, surfaces repositioned into stack coordinates)\n",
+    "- Deriving stack positions from `interstage_lengths` and each stage's physical extent (stages are currently assumed to already share one coordinate frame)\n",
     "- `Mission` — the orchestrator that runs one `Flight` per vehicle configuration with state handoff between them\n",
     "- Deterministic time-based separation (motor burnout + delay) and apogee-triggered deployable ejection\n",
     "- `StochasticMission`\n",