add mat3_transpose() and use it in orbit tracker

- Add mat3_transpose() to physics.h/cpp
- Replace inline transpose in update_orbit_tracker() with function call

src/physics.cpp

@@ -128,6 +128,14 @@ Mat3 mat3_multiply(Mat3 a, Mat3 b) {
     };
 }
 
+Mat3 mat3_transpose(Mat3 m) {
+    return {
+        m.m00, m.m10, m.m20,
+        m.m01, m.m11, m.m21,
+        m.m02, m.m12, m.m22
+    };
+}
+
 Vec3 mat3_multiply_vec3(Mat3 m, Vec3 v) {
     return {
         m.m00 * v.x + m.m01 * v.y + m.m02 * v.z,

src/physics.h

@@ -29,6 +29,7 @@ double vec3_dot(Vec3 a, Vec3 b);
 // Matrix functions
 Mat3 mat3_identity();
 Mat3 mat3_multiply(Mat3 a, Mat3 b);
+Mat3 mat3_transpose(Mat3 m);
 Vec3 mat3_multiply_vec3(Mat3 m, Vec3 v);
 Mat3 mat3_rotation_x(double angle);
 Mat3 mat3_rotation_z(double angle);

src/test_utilities.cpp

@@ -101,11 +101,7 @@ void update_orbit_tracker(OrbitTracker* tracker, CelestialBody* body, CelestialB
         Mat3 rotation = mat3_rotation_orbital(tracker->argument_of_periapsis,
                                               tracker->inclination,
                                               tracker->longitude_of_ascending_node);
-        // Transpose to get inverse rotation (back to orbital plane)
-        Mat3 rotation_T = {rotation.m00, rotation.m10, rotation.m20,
-                           rotation.m01, rotation.m11, rotation.m21,
-                           rotation.m02, rotation.m12, rotation.m22};
-        Vec3 pos_orbital = mat3_multiply_vec3(rotation_T, relative_pos);
+        Vec3 pos_orbital = mat3_multiply_vec3(mat3_transpose(rotation), relative_pos);
         current_angle = atan2(pos_orbital.y, pos_orbital.x);
     } else {
         current_angle = atan2(relative_pos.y, relative_pos.x);