I'm wondering if the following is possible.
Consider some inertial coordiante system x, y, z, and a rotating coordiante system p, q, r defined through matrix rotations as follows.
\begin{pmatrix} p \\ q \\ r \end{pmatrix} = R_1(\theta_1(t)) R_2(\theta_2(t)) R_3(\theta_3(t))...
Hi thanks for the reply.
That's sort of what I'm after but it seems like that solution will give a fixed choice of a such that the boundary conditions will be met. But what if a can change?
Let's use a discrete dynamical system as an example to show what I mean.
Let x_{n+1} = a x_n where a =...
I would advise getting a hold of Solar System Dynamics by Murray and Dermott since there's a lot on resonance and the disturbing function in the book. Since it focuses on the solar system, it covers Jupiters moons, Saturns rings, etc...
Let's say I have a set of nonlinear differential equations of the form.
x' = f(x,y) \\
y' = g(x,y)
Where f and g contain some parameter 'a' that is constrained to within certain values.
Let's say I know x(0), y(0) and x(T), y(T) where T isn't a set value. What methods can I use to...
To add to the above, surely since Mercury will no longer be receiving solar radiation directly, you'd need to take that into account and so the force will likely be halved. You're basically talking about changing Mercurys albedo, I suppose... Sail still has to push Mercurys mass so no great...
Hey D_H, late reply here. Thanks for your post.
Should probably clear up one or two things.
With regards to time step and units used. I suppose I was meaning in terms of finite computer precision and whether certain values 'work better' than others at not accumulating errors.
With...
I've been building a solar system integrator using C++, OpenGL for graphics, Qt for UI and I would like some info about the choice of integrator. The project is at a pretty advanced stage now and I'm currently adding all moons since graphically it's doing well, I can move about the whole system...
Should now say, I've narrowed it down to 2 books which are a bit more general than my specs in the OP but both look like good buys.
Orbital Mechanics by Prussing and Conway.
Fundamentals of astrodynamics and applications by Vallado.
Anyone have any input on which one is better for my...
Hey folks wondering if anyone knows some good books on the following subjects...
Orbital transfers, specifically to Lagrange points with information on stable/unstable manifolds.
Control theory of satellites, new to control theory so perhaps I should be looking at a general control theory...
In this case you have to assume that a is real. Even then the solution will be plus/minus a given that we don't know the sign of a.
evalin(symengine,'assume(a in R_)')
syms x a
int(x/sqrt(x^2+a^2),0,10);
ans =
(a^2 + 100)^(1/2) - abs(a)
Yeah I had thought about black holes. I'd be interested in the less extreme cases such when one of the bodies is a star and the other is not a black hole. My knowledge on this kinda thing is pretty low though and all I really have to go on are luminosity equations for black bodies relating...
Hey folks, I'm trying to find out if a more luminous, less massive body can orbit a more massive, less luminous body (is this an obvious question?). Can such a thing happen? Can it happen in a binary system perhaps..?
By less massive I'd also like to know if it can mean the smaller mass being...
Hey folks, I have an orbit in the circular restricted three body problem with initial conditions
[x(0), 0, z(0), 0, y'(0), 0]
I'm following this paper
http://adsabs.harvard.edu/full/1984CeMec..32...53H
on how to correct these initial conditions given the state transition matrix at a...