Recent content by Daquicker

## \frac {d^2x}{dt} = A - Bx ## ## <=> \frac {d^2x}{dt} + Bx = A ## Then get a characteristic equation for ## \frac {d^2x}{dt} + Bx = 0 ## I suppose? Char. Eq.: ## r^2 + Bx = 0 <=> r = \sqrt{Bx} ## or ## r = - \sqrt{Bx} ## ## => x(t) = C_1 e^{\sqrt{Bx}t} + C_2 e^{- \sqrt{Bx}t}## Then as since...

Last time I had to use one was at least 4 years ago, which is clearly showing. anyways, with position x(t) => v(t) = dx/dt => a(t) = dv/dt = d2x/dt2

With x: distance, t: time, a: acceleration, v: velocity as far as I know with a constant -> integrate a to get v => v = ∫ a dt => v = v0 + at -> integrate v to get x => x = ∫ v dt => x = ∫ (v0 + at) dt => x = x0 + v0t + (at2)/2 <=> a = 2 * (x - x0 - v0t) / t2 with a variable: a(t) => v(t) =...

The only thing I can come up with is: vCraft^2 = vCraftInit + 2∫(xSurf -> X) a(X) dx But I think this isn't correct.

I'll give it another shot tomorrow after a couple hours of sleep, this isn't working after a 26h day. Thankyou for your time so far though :)

Yes, and I agree looking at the problem "from the bottom up" seems like the sensible thing to do as since it gives you a set starting point. Describing a in terms of altitude (xSea) with form A-Bx because it is a linear function is also ok, can do that. => a(xSea) = gPlanet - (cMaxThrustSea -...

The simulation this has to work under is rather symplistic, the atmosphere does scale linearly. The thing I'm stuck on is building up this differential equation. Most, if not all of the information I come across describes acceleration in terms of either time, or velocity. Doing it in terms of...

I edited it so the variable names match.

No, deceleration will not be constant, it will increase as the craft's altitude above planetSeaLevel decreases. If it was constant I could have used EKin = Work and gotten a d from that like i wrote in my post?

The electricity powers an "atmospheric thruster", it's more or less really big "fans". Anyways, it's not supposed to be real world, so this can safely be ignored. Edit: on a rather unrelated sidenote, you did remind me of this article: http://arc.aiaa.org/doi/10.2514/1.B36120

Homework Statement I'm trying to calculate the absolute lowest safe altitude above a planet's surface to start firing the thrusters on a simulated lander in order tot just reach vCraft = 0 at the planet's surface. The force the craft's thrusters responsible for desceleration generate is...