diff --git a/docs/technical_reference.md b/docs/technical_reference.md
index d773100..70e5b2b 100644
--- a/docs/technical_reference.md
+++ b/docs/technical_reference.md
@@ -52,6 +52,16 @@ struct Vec3 {
 };
 ```
 
+### Mat3 (physics.h)
+```cpp
+struct Mat3 {
+    double m00, m01, m02;
+    double m10, m11, m12;
+    double m20, m21, m22;
+};
+```
+Row-major 3x3 matrix for 3D rotation operations.
+
 ### CelestialBody (simulation.h)
 ```cpp
 struct CelestialBody {
@@ -111,7 +121,7 @@ struct OrbitalElements {
     double argument_of_periapsis;
 };
 ```
-**Note:** 3D orientation using `inclination`, `longitude_of_ascending_node`, and `argument_of_periapsis` is defined but not yet applied to orbital calculations (deferred implementation).
+**Note:** 3D orientation is fully implemented using rotation matrices. The rotation sequence is z-x-z Euler angles: R_z(Ω) · R_x(i) · R_z(ω). All 3D parameters are applied in `orbital_elements_to_cartesian()`.
 
 ### Spacecraft (spacecraft.h)
 ```cpp
@@ -184,8 +194,15 @@ struct OrbitTracker {
     double time_at_completion;
     int body_index;
     double min_time_days;
+
+    // Orbital elements for 3D angle calculation
+    double inclination;
+    double longitude_of_ascending_node;
+    double argument_of_periapsis;
+    bool has_orbital_elements;
 };
 ```
+**3D Support:** When `has_orbital_elements` is true, the tracker transforms 3D positions back to the orbital plane using the stored orbital elements before calculating the angle. This enables accurate period measurement for inclined orbits.
 
 ## Module Overview
 
@@ -195,12 +212,24 @@ Vector math and gravity calculations. RK4 (Runge-Kutta 4th order) integration wi
 **Key functions:**
 - `rk4_step(Vec3* position, Vec3* velocity, double dt, double body_mass, double parent_mass)` - RK4 integration using position/velocity pointers
 - `evaluate_acceleration(Vec3 relative_pos, double body_mass, double parent_mass)` - computes gravitational acceleration from parent
+- Matrix operations for 3D orbital orientation:
+  - `mat3_identity()` - returns identity matrix
+  - `mat3_multiply(Mat3 a, Mat3 b)` - matrix-matrix multiplication
+  - `mat3_multiply_vec3(Mat3 m, Vec3 v)` - matrix-vector multiplication
+  - `mat3_rotation_x(double angle)` - rotation about X axis
+  - `mat3_rotation_z(double angle)` - rotation about Z axis
+  - `mat3_rotation_orbital(double omega, double i, double Omega)` - combined z-x-z orbital rotation
+
+**Implementation:**
+- Row-major 3x3 matrix format (different from raylib's column-major 4x4)
+- Rotation matrices follow standard right-hand rule convention
+- Combined orbital rotation: R_z(Ω) · R_x(i) · R_z(ω) for z-x-z Euler angles
 
 ### Orbital Mechanics (orbital_mechanics.cpp/h)
-Keplerian orbital elements to Cartesian coordinate conversion. Supports all orbit types with planar orbits (3D orientation deferred).
+Keplerian orbital elements to Cartesian coordinate conversion. Supports all orbit types with full 3D orientation using rotation matrices.
 
 **Key functions:**
-- `orbital_elements_to_cartesian(OrbitalElements elements, double parent_mass, Vec3* out_position, Vec3* out_velocity)` - converts Keplerian elements to local position/velocity
+- `orbital_elements_to_cartesian(OrbitalElements elements, double parent_mass, Vec3* out_position, Vec3* out_velocity)` - converts Keplerian elements to local position/velocity with 3D orientation
 
 **Implementation:**
 - Circular orbits (e=0): Position on circle, velocity from vis-viva equation
@@ -209,7 +238,7 @@ Keplerian orbital elements to Cartesian coordinate conversion. Supports all orbi
 - Hyperbolic orbits (e>1): Same as elliptical with negative semi_major_axis
 - All elements use SI units (meters, radians)
 - `true_anomaly = 0` is at periapsis (closest approach)
-- 3D orientation (inclination, RAAN, argument of periapsis) defined but not yet applied (deferred)
+- 3D orientation: applies z-x-z Euler rotations (R_z(Ω) · R_x(i) · R_z(ω)) to position and velocity vectors
 
 ### Simulation (simulation.cpp/h)
 Simulation state management and updates. SOI detection using Hill sphere: `r_soi = a * (m/M)^(2/5)`.