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I want to plot the movement of the rocket relative to time ($t$) in the triple dimension $(x, y, z)$. I have all the information about the rocket. I simulate the motion of a rocket. Can you help me to find equations of motion coordinates?

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closed as off-topic by Gert, stafusa, John Rennie, Kyle Kanos, JMac Dec 28 '17 at 18:05

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  • $\begingroup$ Hi Issam, what equations of motion are you looking for? Ascent to orbit, insertion into an orbit, what is the eccentricity of the orbit? You need to be more specific and this might be a question already answered on a computer or space / rocket related SE site. I am not really sure this is the proper place for it. $\endgroup$ – user179430 Dec 27 '17 at 22:06
  • $\begingroup$ Equation of the path of the rocket from the ground to the exit from the atmosphere $\endgroup$ – Issam Otoz Dec 27 '17 at 22:18
  • $\begingroup$ What information do you have about the rocket. I can say without doubt that you don't have all of it. Seeing what you intend to work with will help us provide answers with the correct level of fidelity. After all, rocket science like this can be anywhere from a simple Excel spreadsheet with a few equations, up to a multiple-thousand dollar per seat simulator modeling details that you didn't even know mattered. $\endgroup$ – Cort Ammon Dec 28 '17 at 1:08
  • $\begingroup$ In general one either solves for the general equation of motion or performs a time-steped incremental computation (a "simulation"). In the latter case the only 'equation of motion' that you need is Newton's 2nd law. $\endgroup$ – dmckee Dec 28 '17 at 2:29
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You can use these equations, assuming that the acceleration of the rocket is constant and that air friction is negligible. There are 3 equations, one for the z-axis, which is the up-down axis, one for the y-axis, which is the left-right axis, and one for the x-axis, which is the forward-backward axis. The z-axis equation is: $$z = z_0 + v_0 \sin\theta t + 1/2(g+a\sin\theta) t^2 \;,$$ where $z_0$ is the starting position in the z-axis, $v_0$ is the starting velocity, $\theta$ is the angle between the rocket and the ground, $g$ is the acceleration due to gravity,$t$ is the time, and $a$ is the acceleration of the rocket. The x-axis equation is, $$x =x_0 + v_0(\cos\alpha) t+1/2 (a\cos\alpha) t^2 \;,$$ where $x_0$ is the starting position in the x-axis, $\alpha$ is the angle between the rocket and the x-axis, and t is the time. Finally, the equation for the y-axis is, $$y =y_0 + (v_0\sin\alpha) t+1/2 (a\sin\alpha) t^2 \;,$$ where $y_0$ is the starting position in the y-axis, $\alpha$ is the angle between the rocket and the x-axis, and t is the time. Hopefully those equations help you out in your simulation.

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  • $\begingroup$ I've made a few edits to your math mark up. In particular I have marked up your trig functions as functions (rather than, say, the product of $s$, $i$, and $n$), and block-set your three main equations. Things might be improved further in several ways (using an align environment, for instance), but they are mostly just fiddling around. $\endgroup$ – dmckee Dec 28 '17 at 2:27
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    $\begingroup$ Now, to comment on the physic content, this answer assumes that the orientation of the craft and the acceleration remain constant. As such it is highly artificial if treated as a way to model a while flight. It is however, the starting place for a time-step by time-step simulation. $\endgroup$ – dmckee Dec 28 '17 at 2:31
  • $\begingroup$ Thank you so much Could you give me a reference or pdf to study rocket motion with variable acceleration, and air resistance ?? Where did these wonderful equations come from ?? $\endgroup$ – Issam Otoz Dec 28 '17 at 21:57
  • $\begingroup$ Unfortunately, I cannot give any reference to help you with rocket motion right off the top of my head. I got these "wonderful equations" from my head. If you want more information when it comes to this kind of stuff, try to study on this thing called "projectile motion", that may help. $\endgroup$ – Jake Dec 30 '17 at 23:33

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