Dynamics of flight of the fragments with higher order Haar wavelet method

Abstract

Fragments that have an irregular shape and move at high speeds are difficult to assess since experiments require high-tech solutions, and the differential equations that describe the motion cannot be solved analytically. Different numerical and function approximation methods are used to find the trajectory model. This work uses a state-of-the-art, higher order Haar wavelet method to approximate the trajectory model with empirically determined drag force. The initial conditions of the flight of the fragments are determined by the finite element method. The results obtained by utilizing the Haar wavelet method and the higher order Haar wavelet method are compared. The higher order Haar wavelet method outperforms the Haar wavelet method but allows for keeping the implementation complexity of the method in the same range. Utilizing the higher order Haar wavelet method leads to a reduction in the computational cost since the same accuracy with the Haar wavelet method can be achieved with the use of several order lower mesh.

Keywords

• higher order haar wavelet method
• runge–kutta method
• finite element method
• trajectory
• fragmentation