I'm very new to python but I need to simulate kepler's second law through vpython! I've got the orbit going so far but I don't know how to code the sweeping motion and how to code the r, theta etc. Can anyone help?
http://en.wikipedia.org/wiki/File:Kepler-second-law.gif
this is the kind of thing I want to make! Thank you for your help!
I would define an area variable before the loop along with a time interval (bigger than the dt from the loop's iteration). During the loop, add the small bit of area accumulated during that pass through the loop to the area variable (treat it like a triangle or a circular segment) and wait until the time is evenly divisible by the time interval. At that point, print the area, reset the area variable, and keep going. You should get a list of area values, all close to each other. Vary the time interval to take "bigger chunks" of the orbit, which should also all agree with each other.
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I got an experimental data set that looks more or less like this.
I need to determine how big the hysteresis loop is, aka if I look at two points with the same capacity (Y axis), whats the maximum distance between said points (X axis).
The issue is, data points arent located on the same Y value, aka I cant just find max X and min X for every Y and subtract them - that'd be too easy :^)
I figured I can use convex hull (convhull) to calculate the outer envelope of the set, but then I realised, it will only work for the convex part, not the concaved part, but I guess I can divide my data set into smaller subsets and find a sum of them... or something.
And then, assuming I have the data set thats only the outer outline of the data set, I need to calculate distances between left and right border (as shown here), but then again, thats just data set of X and Y, and Id need to find the point where green line crosses outer rim
So here are the questions:
Is there a matlab procedure that calculates the outer outline of data set, that works with the concaved part - kinda like convhull, but better?
Assuming I have the outline data set, is there an easy way to calculate secant line of data set, like shown on second picture??
Thanks for any advice, hope I made what I have in mind clear enough - english isnt my first language
Benji
EDIT 1: Or perhaps there is an easier (?) way to determine, which points form biggest outline? Like... group points into (duh) groups, lets say, those near 20%, 30%, 40%... and then pick two randomly (or brute force pick all possible pairs), one for top boundary, other for bot boundary, and then calculate area of polygon formed this way? Then, select set of points resulting in polygon with biggest area?
EDIT 2: Ooor I could group them like I thought I would before, and then work on only two groups at a time. Find convex hull for two groups, then for two next groups, and when Im done with all the groups, Id only need to find points common to all the group, and find a global hull :D Yeah, that might work :D
I am using SpriteKit and I need to calculate the fall time of an object (since it changes depending on the screen size). The problem is that the gravity of the scene is given in m/s^2, but all distances are measured in points.
I have tried to find the conversion between points and meters, but it was not very successful.
Any suggestions in how to deal with it?
You may be able to use something like this (A distance calculator written by another on StackOverflow) to calculate the distance between your node and the point directly below it near the ground or another empty node, then plug that distance into an equation to calculate the time.
Unfortunately, I can't give you any code because I've never tried this myself.
I have a missile in my game and I want to keep track of the distance it has traveled to compare against a maximum range.
As it could conceivably travel along a curved path, just comparing its current position against its starting position won't work for me.
I know I can use .magnitude or Vector3.Distance each time through the Update loop, but I also know that's a pretty big performance hit.
I'd appreciate any suggestions.
Thanks Taelsin. For the moment I'm just going to update the distance traveled using magnitude every x number of seconds using Invoke Repeating. It's not exactly performant, but it's simple. Once I get a little more time, I might do what you suggest and perform some simple physics calculations to figure out how long it takes to travel the maximum distance.
When doing SPH, the paper by Kelagar recommends using a particular kernel for pressure induced forces between particles. The kernel it recommends is the following when the radius is within the kernel radius:
(15/(pi*h^9)) * (h - r)^3
where h is the kernel radius, and r is the radius we are interested in calculating the value of a function at.
The paper then states that the gradient of this function is
(-45/(pi*h^9))*((r_vec)/r)*(h-r)^2
where r_vec is now the vector from the center of the kernel to the point we are interested in. As length of r_vec goes to 0 from the positive direction, the paper states that this gradient approaches:
(-45/(pi*h^6))
But this is a scalar, not a vector. In order for there to be a repulsion between the two points we're interested in, there needs to be a direction to repel in.
What direction should we use for when two particles are right next to each other?
I assume that first expression is meant to be a potential. The negative gradient (derivative with respect to r) is then the force. This gradient is a vector, always pointing toward or away from the center. This appears correct for the second expression.
r_vec is, according to what you say, a vector pointing away from the origin to a point at some distance r away. (r_vec/r) is then a unit vector to specify direction. This works at every point except the origin itself, where it can be declared undefined, or declared to be zero. Zero is the average value of (r_vec/r) over all "nearby" points. This means zero force.
Normally in particle simulations with pair-wise forces, we ignore forces of a particle on itself, and of two particle at the same exact position. What about two particle very close, and you have a force law that goes like 1/r, 1/(r^2), or similar? Nobody wants a divide by zero fault. Usually there's a small radius below which the potential is constant matching the given potential formula at the boundary of that radius. Particles too close together have zero force, just so that the simulation won't crash. It may seem unphysical for the force to suddenly cease just inside that boundary when it is fiercely strong just outside it. But we strive to avoid such situations. Keep count of such incidences, and if there are too many, the simulation has gone bad. Maybe a smaller time step is needed.
Luckily you don't have a 1/r type of force, but still you have that nasty r_vec/r whose direction can swing wildly. The same technique of making force zero below a certain tiny radius will help.
But that third expression bothers me. If it's force at r=0, then starting with the force law in the second expression, I'm not sure how the third expression comes about. The problem of it looking scalar while, if it is supposed to be force, expecting vector could be resolved by understanding that it is meant to be the radial component of a force vector. Just multiply the expression by (r_vec/r), the familiar unit-magnitude vector. OTOH, it has no defined direction, so it is nonsense.
Better overall solution: start with a new potential function, one that smoothly levels off and is flat right at r=0, like exp(-r^2) or 1/(1+r^2). The given potential peaks sharply. You want something more like Instead of declaring force zero inside some small zone, the force would just naturally be zero at r=0. Find a flat-at-origin potential that approximates the given one well outside some small radius.
I'm developing a video game for the iPhone. I want each level to save a "ghost" of the best run, just like in Mario Kart.
I've already implemented it, but I used a brute force approach that stores (x, y, rotation) values each frame (60 per second). Needless to say this is very expensive, especially for a mobile device.
I guess I could store the data less often and interpolate when rendering the ghost, but I'm not 100% sure how to do this and if it will look good.
Has anyone done this before? How would you implement it? Is there a standard approach?
Linear interpolation is very easy, if that's what you want. But if the objects you want to interpolate can have non-linear trajectories (from ballistic or lateral accelleration effects) the thing gets more complicated.
The simplest approach would be for you to record the initial position for an object and its movement vector (x,y,z speed, as offsets per time unit). You won't have to record it again for that object until it changes its speed and/or its direction. Then you just record the elapsed time, the new position and the new movement vector (theoretically you don't have to record the position again, just the vectors, but I'd recommend doing so to have a check value - after the program is debugged you can discard it).
Then to playback you place the object at the original position and, for each time frame, add the movement offset to it until it reaches the time for the next recorded position. And so on.