# Numerical Int of ODE in Maple

1. Dec 16, 2009

### 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.

2. Dec 16, 2009

### 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.

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