Classical Theory of Advance of Perihelion of Mercury with Velocity Dependent Inertial and Gravitational Masses

It is shown that Mercury's motion of the perihelion around the Sun, which is believed to be explicable quantitatively only by general relativity, can be fully understood within the frame of the dynamics of special relativity. It is only necessary to take into consideration the relativistic dependence of the planet's inertial and gravitational masses on its velocity (relative to the Sun) in the conservation equations for energy, and linear and angular momenta in the gravitational field. The physical Problem is reduced to a singular, nonlinear differential equation, which is solved numerically for the planet Mercury. The advance of the perihelion of Mercury is shown to be = 42.087' for a period of 100 years, which is in agreement with the as- tronomical observations and the result (by analytical approximations) of general relativity.

Optimal two-iteration sculling compensation mathematical framework for SINS velocity updating

A new two-iteration sculling compensation mathematical framework is provided for modern-day strapdown inertial navigation system（SINS） algorithm design that utilizes a new concept in velocity updating. The principal structure of this framework includes twice sculling compensation procedure using incremental outputs from the inertial system sensors during the velocity updating interval. Then, the moderate algorithm is designed to update the velocity parameter. The analysis is conducted in the condition of sculling motion which indicates that the new mathematical framework error which is smaller than the conventional ones by at least two orders is far superior. Therefore, a summary is given for SINS software which can be designed with the new mathematical framework in velocity updating.

Band-pass filtered velocity statistics in decaying turbulent box

For homogeneous isotropic turbulence study,the acquisition of band-pass filtered velocity increments(FVI) in a non-forced turbulent box is still a challenge both experimentally and numerically.Turbulence and associated physical processes,at a given instant,are permanently contaminated by a forcing process which can seldom be universal.The situation tends to be the origin of intermittency and the non-Gaussian probability density distribution for acceleration and velocity gradients.To reveal implied mechanism,grid turbulence is adapted to observe non-perturbed homogeneous isotropic turbulence.The velocity increments(VI) can be obtained following Comte-Bellot and Corrsin(GCBC) by means of two point-two time shifted velocity measurements.It is difficult to obtain decaying turbulence(DT) at large turbulent Reynolds number without pollution coming from walls.Nevertheless it is also significant to investigate DT in low Reynolds number regimes to determine non-polluted tendencies.The similarity of DT between particle image velocimetry(PIV) and hot wire anemometry measurements by GCBC are presented.Here we focus our tendency on VI and FVI probability density function(PDF) shapes in this letter.In conclusion,the tendency to Gaussian shape in inertial zone wavenumbers,demonstrates that there will be no intermittency if turbulent cascade is not perturbed.

Time-asynchrony identification between inertial sensors in SIMU

Traditional strapdown inertial navigation system （SINS） algorithm studies are based on ideal measurements from gy- ros and accelerometers, while in the actual strapdown inertial measurement unit （SIMU）, time-asynchrony between each iner- tial sensor is inevitable. Testing principles and methods for time- asynchrony parameter identification are studied. Under the single- axis swaying environment, the relationships between the SINS platform drift rate and the gyro time-asynchrony are derived using the SINS attitude error equation. It is found that the gyro time- asynchrony error can be considered as a kind of pseudo-coning motion error caused by data processing. After gyro testing and synchronization, the single-axis tumble test method is introduced for the testing of each accelerometer time-asynchrony with respect to the ideal gyro triad. Accelerometer time-asynchrony parame- ter identification models are established using SINS specific force equation. Finally, all of the relative time-asynchrony parameters between inertial sensors are well identified by using fiber optic gyro SIMU as experimental verification.