How Can I Solve the Rocket Motion Equation Numerically Using Maple?

[Dulle]

Hi there
I'm in desperate need for your help!

I need to solve the rocket motion equation numerically in Maple or some other program. I'm having trouble writing the ODs
in the program.
I have derived the rocket motion equation in a single dimension:

$$\frac {d\vec v_r(t)}{dt} = - \, \frac {\dot m_e(t)} {m_r(t)} \, \vec v_e(t)$$

I assume that the change of mass is constant and the exhaust velocity is constant. Let's say that the rocket has an initial mass of 1 kg, an empty mass of 0.1 kg and the exhaust velocity 5 m/s.

So, i want to solve the equation numerically in Maple or some other program (Maple is preferred) and find the expression for acceleration as a function of time, velocity as a function of time and the altitude as a function of time.

 

[ideasrule]

That equation doesn't look right to me. On the left you have dv/dt, which has units of acceleration, but the right side has units of velocity.

I would approach the problem by considering the rocket in its own reference frame. It ejects a mass dm, with velocity Ve. You can find how fast the rocket moves backwards because of this dm. This speed is of course the "dv", differential change in velocity, in any reference frame.

Once you get an equation, it should be easy to solve analytically.

 

[kerimek]

Hello there,

I understand that you are looking for help with solving the rocket motion equation numerically in Maple or another program. I would be happy to assist you with this task.

To solve the equation numerically, we will need to use a numerical integration method, such as the Euler method or the Runge-Kutta method. These methods approximate the solution to the differential equation by breaking it down into smaller steps and calculating the values at each step.

In Maple, you can use the dsolve command to solve differential equations. For example, you can use the following code to solve the equation you provided:

dsolve({diff(vr(t), t) = -dm(t)/mr(t)*ve(t), vr(0) = 0}, numeric, output = listprocedure, method = rkf45);


This will give you a list procedure that can be used to calculate the velocity at different points in time. You can then use this procedure to calculate the acceleration and altitude at each time step as well.

If you need further assistance with writing the code or understanding the numerical integration methods, please let me know. I would be happy to provide more guidance. Good luck with your project!