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Shooting Type Methods for Solving the two point boundary value problem in the optimization of flight vehicles evolutions
Author(s) -
Istratie V.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19980781547
Subject(s) - shooting method , boundary value problem , initial value problem , convergence (economics) , mathematics , secant method , point (geometry) , differential equation , process (computing) , mathematical optimization , mathematical analysis , computer science , newton's method , geometry , nonlinear system , physics , quantum mechanics , economics , economic growth , operating system
Briefly, a shooting method connst in the repeated solving of the Cauchy problem of the n differential equations, being correlated with a Newton procedure modified by the solving of the equations containing, as unknown, for example, parameters at the initial time resulted due to integration; the number of these equations should be equal with the number of parameters considered and equal with the number of final conditions having fixed values. The parameters are modified during the shooting process and this process is repeated (the convergence being ensured) until the final conditions are checked with a certain imposed error. One determined, the parameters at the initial final time are resulted due to integration. One may remark that the shooting method may also be applied when all the parameters (at the initial and final time) considered. The description of the shooting method, for the clarity of its presentation and of its application manner, will be made based on the concrete case of solving the two point boundary value problem related to the optimization of the hover skip, entry with final maximum velocity at a given azimuth of the space vehicle in the Earth atmosphere.