question 1 should also be of assistance. The aim of this question is that you should write MATLAB code that implements a

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Question 1 Should Also Be Of Assistance The Aim Of This Question Is That You Should Write Matlab Code That Implements A 1 (75.77 KiB) Viewed 28 times

Question 1 Should Also Be Of Assistance The Aim Of This Question Is That You Should Write Matlab Code That Implements A 2 (51.2 KiB) Viewed 28 times

question 1 should also be of assistance. The aim of this question is that you should write MATLAB code that implements a suitable discretization method. Consequently, the use of any standard MATLAB function for solving differential equations, such as ode45 or dsolve, will reduce the marks achieved. 2. The challenge in this exercise is to design and implement an algorithm that calculates the motion of a spacecraft as it lands on the moon. We are going to start the calculations with the spacecraft 10 km above the surface of the moon and assume that its motion is downward relative to the moon, hence we can assume one dimensional motion. The gravitational force on a spacecraft is given by the formula: Mm Fn = -GT! (1) In (1) G represents the universal gravitational constant, which has value 6.67408 109 m2.kg's? M is the mass of the object that is applying a gravitational force to the spacecraft (moon in this case), m is the mass of the spacecraft, r is the vector from the centre of the object (moon) to the spacecraft and r is the magnitude of the vector r. To land at a speed that does not cause damage to the spacecraft, less than 5 ms, there is a need to use thrusters to provide a force to slow the descent. The maximum thrust force a thruster can produce, Tmax, can be calculated using the following formula: Tmax = lsp 90 m (2) In the above equation is represents the specific impulse of the thruster, m is the mass flow rate of fuel to the thruster and go is a reference acceleration normally taken to be the acceleration due to gravity on the earth's surface. Assume that the thrust produced by the thrusters cannot be throttle, that is they are either on, producing maximum thrust, or off, producing no thrust. Efficient use of the thrusters is always an important consideration in any mission. The data required for the program are: Variable Value Mass of spacecraft without fuel, me 7 500 kg Mass of fuel, me 1 500 kg Mass of moon, M 7.34767x102 kg Radius of moon, TM 1 737.4 km Initial altitude, he 10 km Initial speed of spacecraft Oms? Isp 300 s 9.81 m 2 Mass flow rate of fuel summed over all thrusters, m 75 kg s! 90

It might be helpful to know that the spacecraft crashes into the moon at around 180 m s' if the thrusters are not used. a. Describe the steps you went through in understanding the problem and deciding what you will need to include in a design of the solution. (15 Marks) b. Describe your design process. 1. Explain how you converted your understanding to a design? [3 Marks) il. Why did you choose the flow chart, pseudo code or other method to represent your design? (2 Marks iii. Inclusion of pseudo code, flow charts and/or DFDs are all possible ways to do this. Other ways are acceptable as long as they show the ideas that led to your code. I'm not expecting a line by line description but the marks available should indicate I'm expecting more than START -> Input -> Do something -> Output -> END [10 Marks) C. A MATLAB implementation of the program. (30 Marks) d. An explanation of how you tested your implementation. Inclusion of plots or other Information about the results in the answer is expected. (5 Marks/ e. How does the time step size affect the solution? What would you suggest as a suitable time step? Use plots to support your discussion. 15 Marks) Note that the parts to the question match the normal stages of program development Design, Implement, test and investigate (this is also called research) are what any program developer should do.