Apply 3D rotation matrices to orbital elements conversion

- Modify orbital_elements_to_cartesian() to apply z-x-z Euler rotations
- Apply rotation: R_z(Ω) · R_x(i) · R_z(ω) to position and velocity
- Fix generic inclined orbit test: set argument_of_periapsis to π/2
- Molniya position tests now pass with non-zero z-coordinates
- Period test still fails (orbit tracker doesn't handle 3D orbits yet)

src/orbital_mechanics.cpp

@@ -56,6 +56,12 @@ void orbital_elements_to_cartesian(OrbitalElements elements, double parent_mass,
 
     Vec3 velocity = {vx_orbital, vy_orbital, 0.0};
 
-    *out_position = position;
-    *out_velocity = velocity;
+    double omega = elements.argument_of_periapsis;
+    double i = elements.inclination;
+    double Omega = elements.longitude_of_ascending_node;
+
+    Mat3 rotation = mat3_rotation_orbital(omega, i, Omega);
+
+    *out_position = mat3_multiply_vec3(rotation, position);
+    *out_velocity = mat3_multiply_vec3(rotation, velocity);
 }

tests/test_inclined_orbits.cpp

@@ -157,7 +157,7 @@ TEST_CASE("Generic inclined orbit - moderate inclination", "[inclined][generic][
     craft->orbit.true_anomaly = 0.0;
     craft->orbit.inclination = INCLINATION_RAD;
     craft->orbit.longitude_of_ascending_node = 0.0;
-    craft->orbit.argument_of_periapsis = 0.0;
+    craft->orbit.argument_of_periapsis = M_PI / 2.0;
 
     initialize_orbital_objects(sim);