diff --git a/examples/calculate_invariants_position_longtrial.py b/examples/calculate_invariants_position_longtrial.py
index c0cae9d..3b20a65 100644
--- a/examples/calculate_invariants_position_longtrial.py
+++ b/examples/calculate_invariants_position_longtrial.py
@@ -93,14 +93,17 @@
 normalized_progress = False # scale progress to be between 0 and 1
 scale_invariance = False # scale trajectory to unit length, where length is defined by the progress parameter (e.g. arclength)
 ocp_implementation = "rockit" # options: {rockit, optistack}
-solver = "ipopt" # options: {ipopt, fatrop}
-rms_error_tolerance = 1e-1
-solver_options = {"max_iter": 200}
+solver = "fatrop" # options: {ipopt, fatrop}
+rms_error_tolerance = 1e-3
+solver_options = {"max_iter": 500}
 
 # Initialize the InvariantsHandler class with the given options
 ih = invariants_handler.InvariantsHandler(choice_invariants=choice_invariants, trajectory_type=trajectory_type, progress=progress, normalized_progress=normalized_progress, scale_invariant=scale_invariance, ocp_implementation=ocp_implementation, solver=solver, rms_error_tolerance=rms_error_tolerance, solver_options=solver_options)
 invariants, progress, reconstructed_trajectory, moving_frames = ih.calculate_invariants_translation(timestamps, trajectory)
 
+# TODO hide output dummy solve
+# TODO add check constraint violation to see when solver did not converge
+
 # Reconstruct the trajectory from the invariants
 reconstructed_trajectory2, _, _ = ih.reconstruct_trajectory(invariants, position_init=trajectory[0, :], movingframe_init=moving_frames[0, :, :])
 
diff --git a/test_logm_expm.py b/test_logm_expm.py
new file mode 100644
index 0000000..27316bc
--- /dev/null
+++ b/test_logm_expm.py
@@ -0,0 +1,76 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.linalg import logm, expm
+import invariants_py.kinematics.orientation_kinematics as SO3
+import time
+
+# Generate a random skew-symmetric matrix
+omega = SO3.crossmat(np.random.rand(3))
+#omega = SO3.crossmat(np.array([np.pi, 0, 0])) # -- scipy logm fails for this case 
+print("Skew-symmetric matrix omega:")
+print(omega)
+
+# Calculate the exponential of the skew-symmetric matrix using scipy and the custom method
+start_time_scipy_expm = time.time()
+exp_R_scipy = expm(omega)
+end_time_scipy_expm = time.time()
+scipy_expm_duration = end_time_scipy_expm - start_time_scipy_expm
+
+start_time_custom_expm = time.time()
+exp_R_custom = SO3.expm(omega)
+end_time_custom_expm = time.time()
+custom_expm_duration = end_time_custom_expm - start_time_custom_expm
+
+print("Scipy expm:")
+print(exp_R_scipy)
+print(f"Scipy expm duration: {scipy_expm_duration} seconds")
+print("Custom expm:")
+print(exp_R_custom)
+print(f"Custom expm duration: {custom_expm_duration} seconds")
+
+# Calculate the difference between the two exponentials
+diff_exp = exp_R_scipy - exp_R_custom
+frobenius_norm_exp = np.linalg.norm(diff_exp, 'fro')
+print("Difference between expm results:")
+print(diff_exp)
+print(f"Frobenius norm of expm difference: {frobenius_norm_exp}")
+
+# Calculate the logarithm of the rotation matrix using scipy and the custom method
+start_time_scipy_logm = time.time()
+log_R_scipy = logm(exp_R_scipy)
+end_time_scipy_logm = time.time()
+scipy_logm_duration = end_time_scipy_logm - start_time_scipy_logm
+
+start_time_custom_logm = time.time()
+log_R_custom = SO3.logm(exp_R_custom)
+end_time_custom_logm = time.time()
+custom_logm_duration = end_time_custom_logm - start_time_custom_logm
+
+print("Scipy logm:")
+print(log_R_scipy)
+print(f"Scipy logm duration: {scipy_logm_duration} seconds")
+print("Custom logm:")
+print(log_R_custom)
+print(f"Custom logm duration: {custom_logm_duration} seconds")
+
+# Calculate the difference between the two logarithms
+diff_log = log_R_scipy - log_R_custom
+frobenius_norm_log = np.linalg.norm(diff_log, 'fro')
+print("Difference between logm results:")
+print(diff_log)
+print(f"Frobenius norm of logm difference: {frobenius_norm_log}")
+
+# Plot the differences
+plt.figure()
+plt.plot(diff_exp.flatten())
+plt.xlabel('Index')
+plt.ylabel('Difference')
+plt.title('Difference between the two expm results')
+plt.show()
+
+plt.figure()
+plt.plot(diff_log.flatten())
+plt.xlabel('Index')
+plt.ylabel('Difference')
+plt.title('Difference between the two logm results')
+plt.show()