The stability research of numerical solution for rigid body exterior ballistics and fuze mechanical environment in exterior ballistics

DOI:	10.11809/bqzbgcxb2024.11.006
Keywords:	numerical solution; external ballistic calculation; fuze axial overload; integration time step; gear method
Abstract:	Aiming at the stability problem of solving the system of ordinary differential equations of the outer ballistic path of the projectile rigid body and the axial overload of the inertial parts of the fuze, with the help of the computer, we solve the system of ordinary differential equations of the ballistic path of the projectile rigid body and the axial overload of the inertial parts of the fuze with different numerical computation methods and different integration time steps, and then we get the numerical solution for the system of ordinary differential equations of the ballistic path of the projectile rigid body, i.e., the plurals of the ballistic path of the projectile rigid body with the motion of the center of mass and the motion of the plurals around the center of mass.Numerical solutions for axial overloading of fuzed inertial components are obtained on this basis.By extensive simulation, it has been found that when using Runge Kutta method, Adams method, and Gear method to solve the system of ordinary differential equations for rigid exterior ballistics, the elements of center of mass motion converge when the integration time step is set to 0.05 seconds; the element of motion around the center converge when the integration time step is set to 10-4 s.When calculating the peak value of the axial overload sudden change of the inertial component of fuze, it was found that if the peak value is converged, all three methods need to adjust the integration time step to be less than or equal to 10-5 seconds, but in this condition only the Gear method keep correct.
Published:	2024-11-30
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