diff --git a/data/displacement.py b/data/displacement.py
index ed5a492..cecb5c4 100644
--- a/data/displacement.py
+++ b/data/displacement.py
@@ -4,23 +4,18 @@
 
 class Kinematics:
     joints = [] # list of transformation lambdas
-    frames = [np.identity(4)] # list of joint frames in global coordinates
 
     def add_joint(self, joint, frame):
         self.joints.append(joint)
-        self.frames.append(frame)
 
-    def displacement(self, t, move_frames=True):
+    def displacement(self, t):
         disp = np.identity(4)
         for i in range(len(self.joints)):
-            disp = disp @ self.joints[i](t, self.frames[i])
-            if move_frames: 
-                self.frames[i+1] = self.joints[i](t, self.frames[i]) @ self.frames[i+1]
+            disp = disp @ self.joints[i](t)
         return disp
 
     def relative_displacement(self, t0, t1):
-        base = np.linalg.inv(self.displacement(t0, True))
-        return self.displacement(t1, False) @ base
+        return self.displacement(t1) @ np.linalg.inv(self.displacement(t0))
 
 def skew_matrix(v):
     return np.array([
@@ -44,33 +39,47 @@ def rotation_matrix(center, axis, theta):
     mat[:3, 3] = (np.identity(3) - rodrigues) @ center # matvec
     return mat
 
+def rotation_matrix2(axis, theta):
+    axis = np.array(axis)
+    axis = axis / np.sqrt(np.dot(axis, axis))
+    a = np.cos(theta / 2.0)
+    b, c, d = -axis * np.sin(theta / 2.0)
+    return np.array([[a*a + b*b - c*c - d*d, 2*(b*c - a*d), 2*(b*d + a*c), 0],
+                     [2*(b*c + a*d), a*a + c*c - b*b - d*d, 2*(c*d - a*b), 0],
+                     [2*(b*d - a*c), 2*(c*d + a*b), a*a + d*d - b*b - c*c, 0],
+                     [0, 0, 0, 1]])
+
 def move_vertices(vertices, displacement):
     return displacement @ vertices
 
-def displacement_wing(t, frame): return translation_matrix([0, 0, np.sin(0.9 * t)])
-def displacement_freestream(t, frame): return translation_matrix([-1 * t, 0, 0])
-def displacement_rotor(t, frame): return rotation_matrix(frame @ [0, 0, 0, 1], frame @ [0, 0, 1, 0], 1 * t)
-#def displacement_rotor(t, frame): return rotation_matrix([0, 0, 0, 1], [0, 0, 1, 0], 1 * t)
+def displacement_wing(t): return translation_matrix([0, 0, np.sin(0.9 * t)])
+def displacement_freestream(t): return translation_matrix([-2 * t, 0, 0])
+# def displacement_rotor(t, frame): 
+#     return rotation_matrix(frame @ [0, 0, 0, 1], frame @ [0, 0, 1, 0], 1 * t)
+def displacement_rotor(t): 
+    return rotation_matrix([0, 0, 0], [0, 0, 1], 7 * t)
+# def displacement_rotor(t, frame):
+#     return rotation_matrix2([0, 0, 1], 1 * t)
 
 kinematics = Kinematics()
 kinematics.add_joint(displacement_freestream, np.identity(4))
 kinematics.add_joint(displacement_wing, np.identity(4))
-# kinematics.add_joint(displacement_rotor, np.identity(4))
+kinematics.add_joint(displacement_rotor, np.identity(4))
 
-dt = 0.5
-t_final = 15
+dt = 0.01
+t_final = 20
 
 # vertices of a single panel (clockwise) (initial position) (global coordinates)
 vertices = np.array([
-    [0.0, 0.5, 1.0, 1.0], # x
+    [0.0, 2.0, 4.0, 4.0], # x
     [0.0, 10.0, 10.0, 0.0], # y
     [0.0, 0.0, 0.0, 0.0], # z
     [1.0, 1.0, 1.0, 1.0]  # homogeneous coordinates
 ])
+vertices = np.column_stack((vertices, vertices[:,0]))
 
 body_frame = np.identity(4)
 
-vertices = np.column_stack((vertices, vertices[:,0]))
 
 wing_frame = np.identity(4)
 
@@ -83,7 +92,7 @@ def displacement_rotor(t, frame): return rotation_matrix(frame @ [0, 0, 0, 1], f
 ax.set_xlabel('X axis')
 ax.set_ylabel('Y axis')
 ax.set_zlabel('Z axis')
-ax.set_xlim(-15, 0)
+ax.set_xlim(-30, 0)
 ax.set_ylim(-15, 15)
 ax.set_zlim(-5, 5)
 ax.invert_xaxis()  # Invert x axis
@@ -93,14 +102,16 @@ def displacement_rotor(t, frame): return rotation_matrix(frame @ [0, 0, 0, 1], f
 line, = ax.plot3D(vertices[0, :], vertices[1, :], vertices[2, :], 'o-') 
 
 def update(frame):
+    global vertices, kinematics
     t = frame * dt
-    current_displacement = kinematics.relative_displacement(0, t)
-    moved_vertices = move_vertices(vertices, current_displacement)
+    print(f"t = {t:.2f}/{t_final}", end='\r')
+    vertices = move_vertices(vertices, kinematics.relative_displacement(t, t+dt))
     # Update the line object for 3D
-    line.set_data(moved_vertices[0, :], moved_vertices[1, :])  # y and z for 2D part of set_data
-    line.set_3d_properties(moved_vertices[2, :])  # x for the 3rd dimension
+    line.set_data(vertices[0, :], vertices[1, :])  # y and z for 2D part of set_data
+    line.set_3d_properties(vertices[2, :])  # x for the 3rd dimension
     return line,
 
-ani = animation.FuncAnimation(fig, update, frames=np.arange(0, t_final/dt), blit=False)
+ani = animation.FuncAnimation(fig, update, frames=np.arange(0, t_final/dt), blit=False, repeat=False)
+# ani.save('animation.mp4', fps=30, extra_args=['-vcodec', 'libx264'])
 
 plt.show()