Numerical Mathematics Summer 2022 Assignment

Assignment Task

Project 3

A moving rocket can be modeled as an inverted pendulum, because the rocket „,rides" on its jet of fire.

Since the motion takes place in a wider distance from the surface of the earth, gravity can not be considered as constant. Therefore the model needs to take into account the laws of gravitation:

M is the mass of the earth, and m is the mass of the rocket. We assume both masses to be constant. y is the gravitational constant.

r(t) denotes the radial distance from the center of the earth and (1) denotes the angel of the rocket's position.

u(t) denotes the radial part of the thrust and v(t) the angular part.

Your exercise is to steer the SpaceX rocket from the launch pad to the ISS. Assume the ISS is in a circular orbit across the launch pad.

Write a MatLab script, that

• implements the model of the rocket
• defines a final position, given by the motion of the ISS
• defines a time T as time to reach the final position (e.g. by user input)
• computes the path of the rocket
• plots the path of the rocket
• displays the final position and the final velocity

Find functions u(t) and v(t) experimentally that drives the rocket to the final position.

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