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approximate analytical solutions for threedimensional ascent trajectory of a solid-fuel launch vehicle with time-varying mass flow rate

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Chinese Journal of Aeronautics 2024年第10期37卷 275-293页

作者： Qi YU Wanchun CHEN Wenbin YU School of Astronautics Beihang UniversityBeijing 102206China

In the scenario that a solid-fuel launch vehicle maneuvers in outer space at high angles of attack and sideslip for energy management,approximate analytical solutions(AAS)for the threedimensional(3D)ascent flight states are derived,which are the only solutions capable of considering time-varying Mass Flow Rate(MFR)at *** uneven MFR makes the thrust vary nonlinearly and thus increases the difficulty of the problem *** AAS are derived based on a 3D Generalized Ascent Dynamics Model(GADM)with a normalized mass as the independent *** simplify some highly nonlinear terms in the GADM,several approximate functions are introduced carefully,while the errors of the approximations relative to the original terms are regarded as minor ***,a finite series with positive and negative exponents,called Exponent-Symmetry Series(ESS),is proposed for function approximation to decrease the highest exponent in the AAS so as to reduce computer round-off *** calculate the ESS coefficients,a method of seeking the Optimal Interpolation Points(OIP)is proposed using the leastsquares-approximation *** to the artful design of the approximations,the GADM can be decomposed into two analytically solvable subsystems by a perturbation method,and thus the AAS are obtained ***,to help implement the AAS,two indirect methods for measuring the remaining mass and predicting the burnout time in flight are put forward using information from *** results verify the superiority of the AAS under the condition of time-varying MFR.

关键词： approximate analytical solutions 3D ascent trajectory Solid-fuel launch vehicle Uneven thrust Energy management

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approximate analytical solutions for Scattering States of D-dimensional Hulthen Potentials

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Communications in Theoretical Physics 2011年第3期55卷 399-404页

作者： CHEN Chang-Yuan SUN Dong-Sheng LIU Cheng-Lin LU Fa-Lin School of Physics and Electronics Yancheng Teachers University Yancheng 224002 China

Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.

关键词： D-dimensional Hulthen potential Schrodinger equation scattering states approximate analytical solutions

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Large deflection of clamped circular plate and accuracy of its approximate analytical solutions

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Science China(Physics,Mechanics & Astronomy) 2016年第2期59卷 67-77页

作者： Yin Zhang State Key Laboratory of Nonlinear Mechanics(LNM) Institute of Mechanics Chinese Academy of Sciences

A different set of governing equations on the large deflection of plates are derived by the principle of virtual work(PVW), which also leads to a different set of boundary conditions. Boundary conditions play an important role in determining the computation accuracy of the large deflection of plates. Our boundary conditions are shown to be more appropriate by analyzing their difference with the previous ones. The accuracy of approximate analytical solutions is important to the bulge/blister tests and the application of various sensors with the plate structure. Different approximate analytical solutions are presented and their accuracies are evaluated by comparing them with the numerical results. The error sources are also analyzed. A new approximate analytical solution is proposed and shown to have a better approximation. The approximate analytical solution offers a much simpler and more direct framework to study the plate-membrane transition behavior of deflection as compared with the previous approaches of complex numerical integration.

关键词： approximate analytical solutions large deflection plate membrane bulge and blister tests

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Continuum states of modified Morse potential

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Chinese Physics B 2010年第9期19卷 123-128页

作者：卫高峰陈文利 Department of Physics Xi'an University of Arts and Science Department of Basic Science Xi'an Peihua University

Using a proper approximation scheme to the centrifugal term, we study any l-wave continuum states of the Schrodinger equation for the modified Morse potential. The normalised analytical radial wave functions are presented, and a corresponding calculation formula of phase shifts is derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Some numerical results are calculated to show the accuracy of our results.

关键词： modified Morse potential continuum states approximate analytical solutions

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The scattering states of the generalized Hulthén potential with an improved new approximate scheme for the centrifugal term

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Chinese Physics B 2009年第9期18卷 3663-3669页

作者：卫高峰陈文利王红英李院院 Department of Physics Xi'an University of Arts and Science Faculty of Science Xi'an University of Architecture and Technology

This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the 1-wave SchrSdinger equation for the generalized Hulthen potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthen potential and Woods-Saxon potential are also studied briefly.

关键词： generalized Hulthen potential scattering states approximate analytical solutions

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