Recent content by Miner1

I think the problem here is that Kirchhoff's current law produces a set on linearly dependent equations for the loop. You need another independent condition. Kirchhoff's voltage law would, assuming no voltage drop between the nodes, cause the loop to collapse into just a single node. Another...

The problem of finding intersection points of elliptical orbits has been discussed in another thread on this forum - https://www.orbiter-forum.com/showthread.php?t=14828.

What you're asking is called Lambert's problem - given two position vectors and a time of flight, find the unique trajectory that connects the two positions. For your application, one position is the location of Earth at your selected departure date. The second position is the location of Mars...

You can fairly accurately describe a halo orbit using the Poincare-Lindstedt method of successive approximations. As a reference, see Richardson, David L. "Analytic construction of periodic orbits about the collinear points." Celestial mechanics 22.3 (1980): 241-253. This paper also provides...

I think there is confusion as to why the Euler force exists. In your definition of the rotating frame, you have created a constraint that the tangential velocity (in the rotating frame) is zero. This means that all of the forces in this frame must combine together to ensure that this...

Actually, the relative inclination between an orbit with (\Omega_1,i_1) = (50,47) and an orbit with (\Omega_2,i_2) = (0,47) is approximately 36 degrees. cos(i_{rel})=cos(i_1)cos(i_2)cos(\Omega_1-\Omega_2)+sin(i_1)sin(i_2)

The only point of contention I have to your argument is that the dot product of two vectors will always give you the product of the magnitude of the two vectors and the cosine of the small angle between them (small meaning between 0 and \pi). So when finding the angle between two vectors, as...

Actually, when finding the angle between two vectors, using arccosine is the better method. The defined range for the arccosine function is [0,\pi] and this is all you need for this purpose. Notice that in your function VectorMath::angle, the first argument to the atan2 function is cross(aNorm...

Yes, this is the behavior you should expect. The defined range for the arc tangent is (- \frac{\pi}{2}, \frac{\pi}{2}). Also, the tangent function goes to infinity at \frac{\pi}{2}, so if you implement this in software you'd need to do a check that if E is close enough to 180 degrees, set the...

When converting between true anomaly and eccentric anomaly, the best formula to use is tan \frac{E}{2} = \sqrt{\frac{1-e}{1+e}}tan \frac{\nu}{2} Because it involves half-angle tangents, there is no need for quadrant checks for the result will always be in the proper quadrant. I would not...

It sounds like what you are attempting is very similar to Lambert Guidance. That might be something worth looking into.

There's another way to solve this problem that may or may not be more elegant but will certainly generalize the solution if more than three supports exist. Consider a 2D equavalent problem (extension to 3D is straightforward) of a beam loaded with arbitrary masses and supported by multiple...

Or you could do this. Start with the equation for a conic section, i.e. r = \frac{p}{1+e\cos{\nu}} then take the derivative with respect to time to get the radial component of velocity as v_r = \frac{pe\omega\sin{\nu}}{(1+e\cos{\nu})^2} Now multiply and divide by p and use the first...

The radial and along track velocity components are v_r = \frac{\mu e sin\nu}{h} v_\theta = \frac{h}{r} where h = \sqrt[]{\mu a(1-e^2)} You can then use \Omega, i, and \theta = \omega+\nu to transform these components into global coordinates. Hope this helps.

Sorry for taking a while to respond; I've been out of town for a few days. Anyway, the code looks good and I get the same numbers you've posted. When I calculate and plot the intersection points, they line up fairly accurately. You might want to check the code you use to calculate the...