Attitude Angle Simulation Using Quaternion Method for Standard Conic Motion

The quaternion method serves as an efficient mathematical tool for describing 3D object rotation, offering advantages over Euler angles by avoiding gimbal lock issues. It is widely applied in kinematics simulations for aircraft, robotics, and navigation systems. Standard conic motion represents a classic test case for validating attitude algorithm accuracy, characterized by conical rotation around a fixed axis, which generates significant coning errors.

Attitude angle simulation typically involves these implementation steps: First, establish the vehicle kinematic model and define the angular velocity function for conic motion. Under standard conic motion conditions, angular velocity exhibits periodic variation requiring precise discretization in simulation. The attitude update then employs quaternion differential equations, commonly solved using numerical integration methods like second-order Runge-Kutta (RK2) implementation. During each iteration step, special attention must be paid to singularity handling when converting quaternions to Euler angles for output.

The primary challenge lies in coning error compensation, where uncompensated algorithms lead to substantial gyro drift. Practical simulation implementations often employ polynomial extrapolation techniques using angular increments from previous cycles for error correction. Performance evaluation requires comparing theoretical trajectories with simulation results, focusing on statistical deviation characteristics of parameters like pitch and roll angles.

This simulation holds significant importance for inertial navigation system design, validating algorithm robustness under high-maneuver conditions. Extended applications may incorporate sensor noise modeling or comparative analysis with alternative attitude algorithms such as direction cosine matrix methods through Monte Carlo simulations.