Therefore: t he thrust force is dependent on time only. The constant value of the thrust will be known for each rocket model used in the simulation. In other words, the thrust force is a constant up until the time at which the rocket runs out of fuel, after which it is zero. A mathematical representation of the thrust force could be: For the sake of the project, we are assuming that the thrust of the model rocket is constant for the duration of the ascent. For a liquid-fuel rocket, thrust would be controlled during the ascent by a throttle, responding to rocket performance and adjusting thrust over time to control the trajectory. The majority of all rockets which have entered into orbit have been liquid-fuel rockets, as opposed to solid-fuel rockets (the notable exception being the Space Shuttle, which uses both). Finally, we will see the results of this simulation for different rocket models. In this article I will explore each term of the equation of motion, covering the various dependencies that must be accounted for in the code, as well as any assumptions or simplifications made. The equation of motion for a rocket is therefore: The biggest difference between the two problems is that because a rocket’s thrust force is much larger than any damping forces, it will not exhibit chaotic motion like the pendulum. In the case of rocket motion, these forces are represented by the rocket’s weight, atmospheric and wave drags, and its thrust force. At the most basic level, the equation of motion for a rocket can be treated in the same way as the damped driven pendulum - both are affected by three forces: gravitational force, a damping drag force, and a driving force. One example involved the Euler-Cromer method for solving the equation of motion for a pendulum both damped by atmospheric elements and driven by an outside force. In PHYS 375 we have studied several applications for numerical methods in solving otherwise impossible, or at least prohibitively difficult, differential equations.
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