High-Order Radial Derivatives of Harmonic Function and Gravity Anomaly

The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation of gravity anomaly, the Taylor series approach developed in the paper is equivalent theoretically to but more efficient and storage-saving computationally than the well-known gradient operator approach. Numerical simulation shows that Taylor series expansion constructed by the derived formulas for the radial derivatives of gravity disturbance is still convergent for height up to 4 km.

Normal gravity model for inertial navigation of a hypersonic boost-glide vehicle

The normal gravity model of a hypersonic boost-glide vehicle in near space is studied in this paper with the aim of alleviating the influence of the gravity model error on the precision of the inertial navigation system(INS)during flight.First,a spherical harmonic model of the Earth’s gravitational field is introduced and the normal gravity of the Earth is derived from it.Then,the coordinate transformation needed for the application of the gravity model to the near-space navigation algorithm is formulated.Subsequently,the gravity disturbance in near space and the impact of J_(2)and J_(4)gravity truncation errors are analyzed.Finally,different normal gravity models and different precisions of inertial measurement unit(IMU)are exploited to simulate the near-space navigation algorithm.Based on this,the influence of the independent and combined effects caused by the interference factors is analyzed,and the applicable conditions of the normal gravity model are discussed.

Comprehensive compensation method for the influence of disturbing gravity field on long-range rocket guidance computing

With the improvement of the accuracy of the inertial system,the influence of the disturbing gravity field on the accuracy of long-range rocket has become increasingly prominent.However,in actual engineering,there are problems of low accuracy and being time-consuming for disturbing gravity field compensation.In view of this,this paper proposes a set of online comprehensive solutions combining disturbing gravity reconstruction and stellar correction.According to the pre-launch binding parameters,the net function assignment method is used in the navigation system to calculate disturbing gravity in the boost phase online.In the guidance system,a closed-loop guidance online compensation method is proposed based on the state-space perturbation method for the disturbing gravity in the coast phase.At the same time,the vertical deflection can also be corrected by stellar guidance.The calculation results are simulated and verified under different circumstances.Simulation results show that the proposed online compensation algorithm has an accuracy improvement compared with the element compensation algorithm on ground.And the stellar guidance algorithm can further correct the impact deviation.The impact deviation after comprehensive compensation does not exceed 50 m,and the compensation percentage is greater than 65%.

A rapid compensation method for launch data of long-range rockets under influence of the Earth＇s disturbing gravity field

Regarding the rapid compensation of the influence of the Earth＇ s disturbing gravity field upon trajectory calculation,the key point lies in how to derive the analytical solutions to the partial derivatives of the state of burnout point with respect to the launch data.In view of this,this paper mainly expounds on two issues：one is based on the approximate analytical solution to the motion equation for the vacuum flight section of a long-range rocket,deriving the analytical solutions to the partial derivatives of the state of burnout point with respect to the changing rate of the finalstage pitch program;the other is based on the initial positioning and orientation error propagation mechanism,proposing the analytical calculation formula for the partial derivatives of the state of burnout point with respect to the launch azimuth.The calculation results of correction data are simulated and verified under different circumstances.The simulation results are as follows：（1） the accuracy of approximation between the analytical solutions and the results attained via the difference method is higher than 90%,and the ratio of calculation time between them is lower than 0.2%,thus demonstrating the accuracy of calculation of data corrections and advantages in calculation speed;（2） after the analytical solutions are compensated,the longitudinal landing deviation of the rocket is less than 20 m and the lateral landing deviation of the rocket is less than 10 m,demonstrating that the corrected data can meet the requirements for the hit accuracy of a long-range rocket.

A study of PID and L1 adaptive control for automatic balancing of a spacecraft three-axis simulator

Purpose–The three-axis simulator relies on the air film between the air bearing and the bearing seat to achieve weightlessness and the frictionless motion condition,which is essential for simulating the micro-disturbance torque of a satellite in outer space.However,at the beginning of the experiment,the disturbance torque caused by the misalignment between the center of gravity of the simulator and the center of rotation of the bearing is the most important factor restricting the use of the space three-axis simulator.In order to solve this problem,it is necessary to set the balance adjustment system on the simulator to compensate the disturbance torque caused by the eccentricity.The paper aims to discuss these issues.Design/methodology/approach–In this paper,a study of L1 adaptive automatic balancing control method for micro satellite with motor without other actuators is proposed.L1 adaptive control algorithm adds the low-pass filter to the control law,which in a certain sense to reduce the high-frequency signal and speed up the response time of the controlled system.At the same time,by estimating the adaptive parameter uncertainty in object,the output error of the state predictor and the controlled object can be stabilized under Lyapunov condition,and the robustness of the system is also improved.The automatic balancing method of PID is also studied in this paper.Findings–Through this automatic balancing mechanism,the gravity disturbance torque can be effectively reduced down to 10−6 Nm,and the automatic balancing time can be controlled within 7 s.Originality/value–This paper introduces an automatic balancing mechanism.The experimental results show that the mechanism can greatly improve the convergence speed while guaranteeing the control accuracy,and ensuring the feasibility of the large angle maneuver of spacecraft three-axis simulator.