In this study,applications of some analytical methods on nonlinear equation of the launching of a rocket with variable mass are investigated.Differential transformation method(DTM),homotopy perturbation method(HPM)and...In this study,applications of some analytical methods on nonlinear equation of the launching of a rocket with variable mass are investigated.Differential transformation method(DTM),homotopy perturbation method(HPM)and least square method(LSM)were applied and their results are compared with numerical solution.An excellent agreement with analytical methods and numerical ones is observed in the results and this reveals that analytical methods are effective and convenient.Also a parametric study is performed here which includes the effect of exhaust velocity(C_(e)),bum rate(BR)of fuel and diameter of cylindrical rocket(d)on the motion of a sample rocket,and contours for showing the sensitivity of these parameters are plotted.The main results indicate that the rocket velocity and altitude are increased with increasing the C_(e) and BR and decreased with increasing the rocket diameter and drag coefficient.展开更多
文摘In this study,applications of some analytical methods on nonlinear equation of the launching of a rocket with variable mass are investigated.Differential transformation method(DTM),homotopy perturbation method(HPM)and least square method(LSM)were applied and their results are compared with numerical solution.An excellent agreement with analytical methods and numerical ones is observed in the results and this reveals that analytical methods are effective and convenient.Also a parametric study is performed here which includes the effect of exhaust velocity(C_(e)),bum rate(BR)of fuel and diameter of cylindrical rocket(d)on the motion of a sample rocket,and contours for showing the sensitivity of these parameters are plotted.The main results indicate that the rocket velocity and altitude are increased with increasing the C_(e) and BR and decreased with increasing the rocket diameter and drag coefficient.
