1. Use Euler's equations of motion for principal axes in state variable form. Write a MATLAB...

 

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1. Use Euler's equations of motion for principal axes in state variable form. Write a MATLAB program to integrate Euler's equations of motion and solve for x(t), y(t), oz(t) and for Hx(t), Hy(t), and Hz(t) in body-fixed coordinates for an axisymmetric spacecraft with the following PMOIS: Ixx =2887 kg-m I = 2887 kg-m I = 5106 kg-m Assume there no moments (so Mx = My = M = 0) and that the ICs are ox(0) = 0.6 radians/second, co,(0) = 0, and o(0) = 1.1 radians/second. 1a. Make plots of ox (t), oy (t), and o (t) versus time. (You may show all three curves on one plot.) 1b. Make a plot of wy (t) on the vertical axis versus x (t) on the horizontal axis. 1c. Make plots of H, (t), H,(t), and H2(t) versus time. (You may show all three curves on one plot.) 1d. Make a plot of Hy(t) on the vertical axis and Hx (t) on the horizontal axis. le. Describe in words the dynamics of ox (t), y(t), oz(t), Hx(t), H,(t), and H2(t) relative to the body axes. Explain why your results make (or don't make) sense. 1. Use Euler's equations of motion for principal axes in state variable form. Write a MATLAB program to integrate Euler's equations of motion and solve for x(t), y(t), oz(t) and for Hx(t), Hy(t), and Hz(t) in body-fixed coordinates for an axisymmetric spacecraft with the following PMOIS: Ixx =2887 kg-m I = 2887 kg-m I = 5106 kg-m Assume there no moments (so Mx = My = M = 0) and that the ICs are ox(0) = 0.6 radians/second, co,(0) = 0, and o(0) = 1.1 radians/second. 1a. Make plots of ox (t), oy (t), and o (t) versus time. (You may show all three curves on one plot.) 1b. Make a plot of wy (t) on the vertical axis versus x (t) on the horizontal axis. 1c. Make plots of H, (t), H,(t), and H2(t) versus time. (You may show all three curves on one plot.) 1d. Make a plot of Hy(t) on the vertical axis and Hx (t) on the horizontal axis. le. Describe in words the dynamics of ox (t), y(t), oz(t), Hx(t), H,(t), and H2(t) relative to the body axes. Explain why your results make (or don't make) sense.