{'fraction_non_alphanumeric': 0.020984081041968163, 'fraction_numerical': 0.00361794500723589, 'mean_word_length': 5.201793721973094, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
4-degrees of freedom attitude equations of motion: A new approach for simulating flexible satellite dynamics with time-varying payload despite time delay and disturbances

A new approach for the pointing of satellite’s payload is improving the dynamics of satellites to more than 3-DOF. In this approach, there would be no requirement for satellite complete rotations to perform the payload’s mission. The purpose of this study is to derive Four Degrees of Freedom (4-DOF) equations of motion of a satellite and its payload. Therefore, the payload can observe an area of the earth, and simultaneously, the satellite can transfer data to the earth station. Lagrange dynamics are utilized to derive 4-DOF dynamic equations of the system. Then, the system of payload-satellite is controlled by the sliding mode control method with three different sliding functions. Environmental disturbances and appropriate time delay for Low Earth Orbit are applied to the nonlinear attitude equations. Numerical simulations demonstrate the effectiveness of the 4-DOF nonlinear dynamics of the payload-satellite system and indicate that the controller negates the effects of the nonlinear external disturbances and time delay. According to the results, the attitude states attain the reference targets of Euler angles and the time-varying payload with excellent precision and high convergence speed.