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This paper concentrates on the numerical solution of the exterior trajectory of grenades.We consider the model with six degrees of freedom,which is an initial value problem of an ordinary differential system with twelve variables.Due to the high oscillating property of the equations,only very small time steps must be used when the explicit Runge-Kutta methods are applied,which leads to an unsatisfying efficiency.In this paper,we use the skill of asymptotic expansion to obtain the analytical expressions of the approximate solutions of two variables.Thus the oscillations in the solutions are significantly reduced,and the time step can be enlarged intrinsically.Numerical examples show that the efficiency is effectively enhanced by this method.
This paper concentrates on the numerical solution of the exterior trajectory of grenades. We consider the model with six degrees of freedom, which is an initial value problem of an ordinary differential system with twelve variables. Due to the high oscillating property of the equations, only very small time steps must be used when the explicit Runge-Kutta methods are applied, which leads to an unsatisfying efficiency.In this paper, we use the skill of asymptotic expansion to obtain the analytical expressions of the approximate solutions of two variables.Thus the oscillations in the solutions are significantly reduced, and the time step can be enlarged intrinsically. Numerical examples show that the efficiency is effectively enhanced by this method.