Recent content by spaderdabomb

Well I was mostly referring to the exact equation when I said I couldn't think of anything in nature that models it. But...depends what you call nature. The discharge time of a capacitor? Well...that follow this equation multiplied by a few constants almost exactly. But does that count as...

I don't think it is necessarily a better approximation for drag. I mean I guess it depends what you are comparing it too? Certainly there are better models of drag (although, have you know it, the Navi-Stokes Millenium problem deals with this exact problem, and it hasn't been solved!). But on...

Think I figured it out. All I had to do was write a program that constantly gave the difference in the euler angles of the two coordinate systems. Then I took the original vector (pointing in the -z direction of my probe's coordinate system) and did the inverse transformation using the inverse...

I'm doing a research project currently and basically what I have is a camera measuring a probe. I have designed the camera to give the orientation of the probe using euler angles in the camera's frame of reference. This was working for most of my data, but now I need a 3-D visualization of what...

I would form a matrix. You should get a 3x1 on the left side equaled to a 3x3 times some constants that you need to solve for. Solve for the eigenvalues and eigenvectors.

Well I think it does have to do with the number of times you differentiate in a way, but in other cases it could depend on your coefficients (sorry I know I previously told you to forget about coefficients, but in some rarer cases such as this one it can come up). Think about the top equation...

Also from your previous post I just wanted to make sure that you knew that you don't just "discard" a solution. That imaginary solution you obtained was no solution at all...I checked and it did not satisfy the initial equation. It is simply not a solution, rather than a solution you just discard.

You are supposed to guess to some extent, but it should be a VERY good guess (or in other words...there is a method to this madness that should get you the right guess almost every time). to keep it simple, your Y(t) should take on a similar form in terms of its functions. So what I mean is...

Well look at it this way. If you cube your solutions of r, you should get -1. What is (-1)^3? Well, (-1). That tells me that (-1) MUST be a solution

Are you sure your r values are correct? Now that I am looking back over it I would think that r = (-1) should be one of your values since in your characteristic equation you get r^3 = -1 If r = -1 then were in business!

So your last value should fit the form Ce^{rt} for this particular problem. Since your value is r = -1/2 + 3i/√2, we get e^{(-1/2 + 3i/√2)t}. This still presents a problem though hmmm

Well you have your values for the homogeneous solution, so now you need to find the values for your particular solution. There are a number of methods that apply to higher order differential equations that are the same for second order differential equations. Try using one of those methods. Then...

Im not sure which images you are talking about...you sure they were uploaded correctly?

Sorry double posted by accident

Using energy is definitely the right way to go about it. Start off with the fact that the center of mass is 0 potential energy for both objects. You should be able to find a useful relationship between m_1, m_2, r_1 and r_2. Next you will probably want to compare the kinetic energy of the two...