orbital | Experimental PlayStation 4 emulator | Emulator library
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Virtualization-based PlayStation 4 emulator.
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QUESTION
I am writing a 2D simulator and game using the HTML canvas which involves orbital mechanics. One feature of the program is to take the position and velocity vector of a satellite at one point and return the semi-major axis, eccentricity, argument of periapsis, etc of a 2D orbit around one planet. When the eccentricity is less than one, I can easily graph the orbit as an ellipse using ctx.ellipse(). However, for eccentricities greater than one, the correct shape of the orbit is a hyperbola. At the moment, my program just draws nothing if the eccentricity is greater than one, but I would like it to graph the correct hyperbolic orbit. Since there is no built in "hyperbola" function, I need to convert my orbit into a Bézier curve. I am at a bit of a loss as to how to do this. The inputs would be the location of one focus, semi-major axis, eccentricity, and argument of periapsis (basically how far the orbit is rotated) and it should return the correct control points to graph a Bézier curve approximation of a hyperbola. It does not have to be exactly perfect, as long as it is a close enough fit. How can I approach this problem?
...ANSWER
Answered 2021-May-12 at 15:45In terms of conic sections, hyperbola are unfortunately the one class of curves that the Canvas cannot natively render, so you're stuck with approximating the curve you need. There are some options here:
- Flatten your curve, by sampling the hyperbola at one or two points in the distance and lots of points near the extrema so that you can draw a simple polygon that looks like a curve.
- Model the hyperbola with a single "best approximation" quadratic or cubic curve.
- As @fang mentions: sample the curve at a few points and convert the Catmull-Rom spline through those points to Bezier form.
- Combine approaches 1 and 2. using a single Bezier curve to approximate the part of the hyperbola that actually looks curved, and using straight lines for the parts that don't.
- Combine approaches 1 and 3, using a Catmull-Rom spline for the curvy bit, and straight lines for the straight bits.
Curve flattening is basically trivial. Rotate your curve until it's axis-aligned, and then just compute y
given x
using the standard hyperbolic function, where a
is half the distance between the extrema, and b
is the semi-minor axis:
QUESTION
ANSWER
Answered 2021-Apr-12 at 21:22Try adding to your th and td
QUESTION
I’m learning python and dash and I’m building an application for monitoring my trading.
I’ve adapted the code from : “Live Updating Components” example (Orbital Satellite). It works well on jupyter notebook and repl.it but I have an error when I try it on my computer :
"Traceback (most recent call last): File "orbital.py", line 62, in Input('interval-component', 'n_intervals'))"
“The input argument interval-component.n_intervals must be a list or tuple of dash.dependencies.Inputs.”
I don’t understand why
Here is my code :
...ANSWER
Answered 2021-Apr-04 at 15:14As the error is trying to say, you need to wrap your Input
in a list, like this:
QUESTION
I created a simple view designed to show the content of an array that is stored in an Observable Object property:
...ANSWER
Answered 2021-Jan-11 at 22:03If your data is dynamic (will change while the view is on screen) you need to give each item an ID so that the view knows when to update.
METHOD 1: You can give it a local ID by just changing your ForEach loop:
QUESTION
I made a line mesh with elliptical shape, representing the orbit wiht eccentricity e, and semi-major axis a. The mesh is a child of a group called orbitGroup that contains other objects. Also, I added a gui to change this parameters. Every time gui changes it calls the next function:
...ANSWER
Answered 2021-Jan-19 at 00:49You should be able to replace the vertex (position
) buffer and call it a day.
QUESTION
I have a function that takes orbital parameters and texture images from a dataset and creates a 3d object (a planet). However for some reason textures aren't being rendered. Using BasicMaterial it works normally, but not with StandardMaterial or PhongMaterial. (There is a point light in the scene), I already tested the textures outside the loop and the function, they work nice. I don´t know what else to do. I let here the code.
...ANSWER
Answered 2021-Jan-06 at 16:45var tex = texture.clone();
When doing this, can you please add the following line?
QUESTION
I'm in a project in my University and I have to implement the Runge-Kutta 4-order integrator using Python. I know I can use for example Sympy, but the goal here is implement the method, the code is ready written in Fortran language, so basically I have a data base with the correct values of solutions and I have to get similar solutions in my code. However, we have some problems; I did the same several times using linear equations ( first and second order ), however this is a second order nonlinear equation from Newton universal law of gravitation. The code has no error, my problem is what my code is doing wrong that I cannot get the right results.
Below I'll show some of the expected values and the ones i'm getting, after them I'll show the code.
I'd be really pleasured if someone could help me.
RIGHT RESULTS (expected results)
...ANSWER
Answered 2020-Nov-17 at 10:46The inventor of the Runge-Kutta methods was really named Martin Wilhelm Kutta. (Runge 1895 did something strange, Heun 1900 made it less strange, Kutta 1901 made it fully flexible and systematic.)
You have a severe conceptual error in your implementation.
- You need to treat a coupled system as a coupled system, you can not de-couple the integration of the components. At best you will get a first order integrator this way.
- This is especially visible and egregious in your use of
R3
. This value needs to be re-computed for every stage. If the derivatives vector depends on a function of the state, then this value can not be constant.
See Cannot get RK4 to solve for position of orbiting body in Python and Is there a better way to tidy this chuck of code? It is the Runge-Kutta 4th order with 4 ODEs for working code examples.
QUESTION
Hi all I am working on rocket trajectory optimization with Dymos. The equations of motion for my model are for a spherical non-rotating Earth
where v is speed of the rocket, gamma is the flightpath angle to local horizontal, h is height above surface, theta is angle along the great circle of the trajectory, m is mass, epsilon is angle of attack, T is trust, D is drag, L is lift. These are quite similar to the equations of motion in the Dymos water rocket example. I used check_partials and my analytic derivatives seem to be correct.
As you can see gamma's rate of change is divided by v, so you have a singularity where v=0 at the beginning of the trajectory. You can get around that by starting v at some small number that's a small fraction of the intended final velocity -- like 1 to m/s for an orbital rocket.
However, the lower I set my initial velocity, the harder I can see the optimizer and grid refinement needs to work to get to a converged solution. For example,
setting final conditions of h=200 km, v= 7668 m/s and gamma=0 (a circular orbit), with v initial = 10 m/s, I have to start with 20 segments of order 6 to be able to reach convergence, and the final grid is like this
Number of Segments = 25 Segment Ends = [-1.0, -0.9833, -0.9667, -0.95, -0.9333, -0.9, -0.85, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0] Segment Order = [9, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
The optimization time on this converged grid is 45 seconds
if I use v_initial = 1000 m/s, same final conditions, and a starting grid of 20 segments of order 3, the final grid is
Segment Ends = [-1.0, -0.95, -0.9, -0.8, -0.7, -0.6, -0.4, -0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0] Segment Order = [6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3]
the optimization time on the converged grid is 3.18 seconds.
Given the way grid points are being concentrated towards the beginning of the trajectory makes me think that the singularity in gamma_dot caused by v is the problem.
What can I do to improve performance?
...ANSWER
Answered 2020-Dec-11 at 10:08I agree that the singularity here is a problem, and your approach of setting it to some small initial value is generally a good way to go.
While they're generally pretty reasonable, the grid refinement algorithms currently in Dymos might have issues when the EOM start going singular, and I think you're seeing that here.
What else can you try?
-You could break the problem into multiple phases. The first phase would cover the vertical ascent before pitchover begins. By using a set of EOM that are non-singular for this phase of the trajectory, you could allow the vehicle to build up some speed before transitioning to the second phase, using your current EOM.
-You could reformulate the problem to use EOM that don't have a singularity near your operating conditions. Flight path EOM are generally nice and benign, but they suffer from singularities at v=0 (and gamma=+/-90 deg in the 3D case).
A Cartesian formulation to the EOM, where the vehicle inertial position and velocity are [x, y, vx, vy], would provide EOM that are only singular at the center of the planet. Parameterizing the initial states is somewhat more tricky (especially in the 3D case) because the initial velocity is the initial velocity of the launch pad fixed to the rotating Earth.
You could also try treating flight path angle as a fixed parameter for the first phase, fixing it to 90 degrees until some adequate velocity is established. In this case you'd be accepting some small inaccuracy in your dynamics in order to get better behavior.
QUESTION
I'm trying to embed an orbital simulation into a tkinter frame, I have the plot working properly I am now just trying to input circles into the graph to represent planets. I have had a look for documentation on how to draw circles in FigureCanvasTkAgg but can't find anything and was hoping someone could help.
Here's the code:
...ANSWER
Answered 2020-Dec-09 at 10:08Axes
instances do not have a Circle
method. That is part of matplotlib.patches
, and can be imported separately.
Also, when you add the patch to the ax
, you don't need to do ax.gca()
, since you already have a handle for the current Axes (i.e. no need to .gca()
, which stands for get current axes).
Finally, Axes
do not have a show()
method. That is a function from the pyplot module, that can be called as plt.show()
If you don't have them already, add the following imports:
QUESTION
Context: I am not sure if this is the right site to post this question, please let me know if it isn't. My aim is to solve the coupled differential equations given in the code for the Alpha Centauri star system.
Code:
...ANSWER
Answered 2020-Nov-17 at 10:28You need to read and understand the documentation. mpmath.odefun
is fundamentally different from scipy.integrate.odeint
. mpmath.odefun
provides a dynamical solution object more similar to the scipy.integrate.ode
stepper class in that at its call it does not compute (much), it simply initializes an object. The actual solution data in form of a "dense output" is computed and stored in subsequent calls to the returned object. The time range of that data is extended as necessary.
How that is done can be seen in the documentation examples. In your case this could be done as
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