1 Assignment and Requirements 1.1 Assignment According to the rocket parameters and standard program angle, complete the standard ballistic simulation under the launch system by MATLAB or C++. 1.2 Requirements (1) Source procedures and reports shall be provided; (2) The report shall include simulation results of nominal trajectory, including but not limited to altitude, speed, angle and other curves, etc.; 2 The Relevant Equations 2.1 Simplified dynamics equation Assuming that the earth is a homogeneous sphere, only considering the influence of axial thrust, aerodynamic force and gravity of the engine, and adopting small angle hypothesis and instantaneous equilibrium hypothesis, the following dynamic equation can be established in the launch system: dvx/dtdvx/dtdvz/dt=m1coscossincossinsincos0cossinsinsincosPCAqSMCqSM57.3CzqSM57.3+r3xy+Rzdv/dtdy/ctd/dt=vxvyvz Table 1 Symbol definitions and standard values Nominal case without homing, rocket tracking standard procedure angle =PV=P 2.3 Supplementary Equation =arctanvxvvv=arcsinvvz Note: To avoid singularity in calculation of initial value and v, you can directly set the initial value of to 90 and the initial value of r, to 0 . ==r 2.3.2 Thrust equation The engine thrust equation is P=Ipm+Se(p0ph) 2.3.3 Atmospheric Model Local atmospheric pressure and atmospheric density are both functions of height, for details, US 1976 Model is used in this assignment. 2.3.4 Mass Equation m=m0mt 2.3.5 Other Equations v=vx2+vy2+vz2r=x2+(y+R)2+z2h=rRq=21v2 Some of the data is given in Table 1, and the rest is shown below. 3.1 Initial value and shutdown time The initial values of x,y,z,vx,vy,vz are 0 . The standard shutdown time is 145s 3.2 Standard procedure Angle See the appendix "Standard Program Angle Interpolation Table". Interpolation of time in nominal case. Note that if the interpolation exceeds the boundary, the boundary value must be taken, that is, the interpolation cannot be extrapolated. \begin{tabular}{|c|c|c|c|} \hline A & B & C \\ \hline time (after take off) & & & \\ \hline s & & \\ \hline 0 & 90 & 0 \\ \hline 1 & 89.9994 & 0.00309 \\ \hline 2 & 89.9988 & 0.00619 \\ \hline 3 & 89.9981 & 0.00928 \\ \hline 4 & 89.9975 & 0.01237 \\ \hline 5 & 89.9969 & 0.01547 \\ \hline 6 & 89.9963 & 0.01856 \\ \hline 7 & 89.9957 & 0.02165 \\ \hline 8 & 89.995 & 0.02475 \\ \hline 9 & 89.9944 & 0.02784 \\ \hline 10 & 89.9938 & 0.03094 \\ \hline 11 & 89.9677 & 0.03404 \\ \hline 12 & 89.9447 & 0.03715 \\ \hline 13 & 89.9085 & 0.04027 \\ \hline 14 & 89.8573 & 0.0434 \\ \hline 15 & 89.7893 & 0.04655 \\ \hline 16 & 89.7036 & 0.04972 \\ \hline \end{tabular}