MNT: Refactor inertia calculations using parallel axis theorem

CHANGELOG.md

@@ -39,6 +39,7 @@ and this project adheres to [Semantic Versioning](http://semver.org/).
 
 - MNT: Refactor flight prints module [#579](https://github.com/RocketPy-Team/RocketPy/pull/579)
 - DOC: Convert CompareFlights example notebooks to .rst files [#576](https://github.com/RocketPy-Team/RocketPy/pull/576)
+- MNT: Refactor inertia calculations using parallel axis theorem [#573] (https://github.com/RocketPy-Team/RocketPy/pull/573)
 - ENH: Optional argument to show the plot in Function.compare_plots [#563](https://github.com/RocketPy-Team/RocketPy/pull/563)
 
 ### Fixed

rocketpy/motors/hybrid_motor.py

@@ -1,3 +1,5 @@
+from rocketpy.tools import parallel_axis_theorem_from_com
+
 from ..mathutils.function import Function, funcify_method, reset_funcified_methods
 from ..plots.hybrid_motor_plots import _HybridMotorPlots
 from ..prints.hybrid_motor_prints import _HybridMotorPrints
@@ -455,22 +457,21 @@ def propellant_I_11(self):
         ----------
         .. [1] https://en.wikipedia.org/wiki/Moment_of_inertia#Inertia_tensor
         """
-        solid_correction = (
-            self.solid.propellant_mass
-            * (self.solid.center_of_propellant_mass - self.center_of_propellant_mass)
-            ** 2
-        )
-        liquid_correction = (
-            self.liquid.propellant_mass
-            * (self.liquid.center_of_propellant_mass - self.center_of_propellant_mass)
-            ** 2
-        )
 
-        I_11 = (
-            self.solid.propellant_I_11
-            + solid_correction
-            + self.liquid.propellant_I_11
-            + liquid_correction
+        solid_mass = self.solid.propellant_mass
+        liquid_mass = self.liquid.propellant_mass
+
+        cm = self.center_of_propellant_mass
+        solid_cm_to_cm = self.solid.center_of_propellant_mass - cm
+        liquid_cm_to_cm = self.liquid.center_of_propellant_mass - cm
+
+        solid_prop_inertia = self.solid.propellant_I_11
+        liquid_prop_inertia = self.liquid.propellant_I_11
+
+        I_11 = parallel_axis_theorem_from_com(
+            solid_prop_inertia, solid_mass, solid_cm_to_cm
+        ) + parallel_axis_theorem_from_com(
+            liquid_prop_inertia, liquid_mass, liquid_cm_to_cm
         )
 
         return I_11

rocketpy/motors/liquid_motor.py

@@ -7,6 +7,7 @@
     funcify_method,
     reset_funcified_methods,
 )
+from rocketpy.tools import parallel_axis_theorem_from_com
 
 from ..plots.liquid_motor_plots import _LiquidMotorPlots
 from ..prints.liquid_motor_prints import _LiquidMotorPrints
@@ -388,10 +389,9 @@ def propellant_I_11(self):
         for positioned_tank in self.positioned_tanks:
             tank = positioned_tank.get("tank")
             tank_position = positioned_tank.get("position")
-            I_11 += (
-                tank.inertia
-                + tank.fluid_mass
-                * (tank_position + tank.center_of_mass - center_of_mass) ** 2
+            distance = tank_position + tank.center_of_mass - center_of_mass
+            I_11 += parallel_axis_theorem_from_com(
+                tank.inertia, tank.fluid_mass, distance
             )
 
         return I_11

rocketpy/motors/motor.py

@@ -7,7 +7,7 @@
 from ..mathutils.function import Function, funcify_method
 from ..plots.motor_plots import _MotorPlots
 from ..prints.motor_prints import _MotorPrints
-from ..tools import tuple_handler
+from ..tools import parallel_axis_theorem_from_com, tuple_handler
 
 try:
     from functools import cached_property
@@ -513,25 +513,19 @@ def I_11(self):
         ----------
         .. [1] https://en.wikipedia.org/wiki/Moment_of_inertia#Inertia_tensor
         """
-        # Propellant inertia tensor 11 component wrt propellant center of mass
-        propellant_I_11 = self.propellant_I_11
 
-        # Dry inertia tensor 11 component wrt dry center of mass
+        prop_I_11 = self.propellant_I_11
         dry_I_11 = self.dry_I_11
 
-        # Steiner theorem the get inertia wrt motor center of mass
-        propellant_I_11 += (
-            self.propellant_mass
-            * (self.center_of_propellant_mass - self.center_of_mass) ** 2
-        )
+        prop_to_cm = self.center_of_propellant_mass - self.center_of_mass
+        dry_to_cm = self.center_of_dry_mass_position - self.center_of_mass
 
-        dry_I_11 += (
-            self.dry_mass
-            * (self.center_of_dry_mass_position - self.center_of_mass) ** 2
+        prop_I_11 = parallel_axis_theorem_from_com(
+            prop_I_11, self.propellant_mass, prop_to_cm
         )
+        dry_I_11 = parallel_axis_theorem_from_com(dry_I_11, self.dry_mass, dry_to_cm)
 
-        # Sum of inertia components
-        return propellant_I_11 + dry_I_11
+        return prop_I_11 + dry_I_11
 
     @funcify_method("Time (s)", "Inertia I_22 (kg m²)")
     def I_22(self):

rocketpy/rocket/rocket.py

@@ -18,6 +18,7 @@
 )
 from rocketpy.rocket.components import Components
 from rocketpy.rocket.parachute import Parachute
+from rocketpy.tools import parallel_axis_theorem_from_com
 
 
 class Rocket:
@@ -619,6 +620,10 @@ def evaluate_dry_inertias(self):
         ----------
         .. [1] https://en.wikipedia.org/wiki/Moment_of_inertia#Inertia_tensor
         """
+        # Get masses
+        motor_dry_mass = self.motor.dry_mass
+        mass = self.mass
+
         # Compute axes distances
         noMCM_to_CDM = (
             self.center_of_mass_without_motor - self.center_of_dry_mass_position
@@ -628,18 +633,18 @@ def evaluate_dry_inertias(self):
         )
 
         # Compute dry inertias
-        self.dry_I_11 = (
-            self.I_11_without_motor
-            + self.mass * noMCM_to_CDM**2
-            + self.motor.dry_I_11
-            + self.motor.dry_mass * motorCDM_to_CDM**2
+        self.dry_I_11 = parallel_axis_theorem_from_com(
+            self.I_11_without_motor, mass, noMCM_to_CDM
+        ) + parallel_axis_theorem_from_com(
+            self.motor.dry_I_11, motor_dry_mass, motorCDM_to_CDM
         )
-        self.dry_I_22 = (
-            self.I_22_without_motor
-            + self.mass * noMCM_to_CDM**2
-            + self.motor.dry_I_22
-            + self.motor.dry_mass * motorCDM_to_CDM**2
+
+        self.dry_I_22 = parallel_axis_theorem_from_com(
+            self.I_22_without_motor, mass, noMCM_to_CDM
+        ) + parallel_axis_theorem_from_com(
+            self.motor.dry_I_22, motor_dry_mass, motorCDM_to_CDM
         )
+
         self.dry_I_33 = self.I_33_without_motor + self.motor.dry_I_33
         self.dry_I_12 = self.I_12_without_motor + self.motor.dry_I_12
         self.dry_I_13 = self.I_13_without_motor + self.motor.dry_I_13
@@ -696,18 +701,14 @@ def evaluate_inertias(self):
         CM_to_CPM = self.center_of_mass - self.center_of_propellant_position
 
         # Compute inertias
-        self.I_11 = (
-            self.dry_I_11
-            + self.motor.I_11
-            + dry_mass * CM_to_CDM**2
-            + prop_mass * CM_to_CPM**2
-        )
-        self.I_22 = (
-            self.dry_I_22
-            + self.motor.I_22
-            + dry_mass * CM_to_CDM**2
-            + prop_mass * CM_to_CPM**2
-        )
+        self.I_11 = parallel_axis_theorem_from_com(
+            self.dry_I_11, dry_mass, CM_to_CDM
+        ) + parallel_axis_theorem_from_com(self.motor.I_11, prop_mass, CM_to_CPM)
+
+        self.I_22 = parallel_axis_theorem_from_com(
+            self.dry_I_22, dry_mass, CM_to_CDM
+        ) + parallel_axis_theorem_from_com(self.motor.I_22, prop_mass, CM_to_CPM)
+
         self.I_33 = self.dry_I_33 + self.motor.I_33
         self.I_12 = self.dry_I_12 + self.motor.I_12
         self.I_13 = self.dry_I_13 + self.motor.I_13

rocketpy/tools.py

@@ -382,6 +382,33 @@ def check_requirement_version(module_name, version):
     return True
 
 
+def parallel_axis_theorem_from_com(com_inertia_moment, mass, distance):
+    """Calculates the moment of inertia of a object relative to a new axis using
+    the parallel axis theorem. The new axis is parallel to and at a distance
+    'distance' from the original axis, which *must* passes through the object's
+    center of mass.
+
+    Parameters
+    ----------
+    com_inertia_moment : float
+        Moment of inertia relative to the center of mass of the object.
+    mass : float
+        Mass of the object.
+    distance : float
+        Perpendicular distance between the original and new axis.
+
+    Returns
+    -------
+    float
+        Moment of inertia relative to the new axis.
+
+    Reference
+    ---------
+    https://en.wikipedia.org/wiki/Parallel_axis_theorem
+    """
+    return com_inertia_moment + mass * distance**2
+
+
 # Flight