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  1. M

    An update on all things Lissajous and Halo

    The short answer is: yes. However, a bunch of more practical issues (associated with macro-economic concerns and, of course, COVID-19) have stolen much of my attention for the last year or so. At some point, I'm sure, I'll find the time to focus on all things Lissajous once again. Regards
  2. M

    Numerical calculation of the Earth-Moon L2 halo orbit family

    Hi, ShoorDrag Sorry, I don't maintain a webpage or github repository. If I recall, I generated the stable manifold trajectory example using a time reversal trick: let's suppose you that you know the centre-manifold trajectory (e.g.,, by using the L-P expansion scheme as discussed above.)...
  3. M

    Numerical calculation of the Earth-Moon L2 halo orbit family

    Hi, ShootDrag I've attached my Mathematica notebook. This has been added with a '.txt' suffix rather that a '.nb' notebook suffix in order to 'fool' this forum's file uploading service. I suggest that after downloading, you change the file extension back to '.nb' from '.txt'. This notebook...
  4. M

    Numerical calculation of the Earth-Moon L2 halo orbit family

    Hi, ShootDrag Not sure what your level of mathematical background is - but the basic scheme I used as a starting point was the paper: "High-order solutions of invariant manifolds associated with libration point orbits in the elliptic restricted three-body system". I've attached a copy of this...
  5. M

    calculating relative inclination

    Yes, this is the correct expression for the relative inclination.
  6. M

    News Raspberry Pi computer, is it rational?

    I thought I might chip into this discussion. I've recently bought a Raspberry Pi 4 - 4 GB RAM, quad core ARM processor; 1.5 GHz. It has one Gigabit Ethernet port; two USB-3 ports; two USB-two ports; one USB-C port; wifi; bluetooth. The operating card is, by default, confined to an micro-SD...
  7. M

    Textbook Recommendation, Calculus of Variations

    I don't have a recommended textbook, but here's my potted version of Calculus of Variations: Let's suppose that you have a function that is written as the integral: S = \int_a^b L\left(y(x), y'(x)\right)\,dx This reads as 'the integral (over x) of some function, L, that is itself a function...
  8. M

    A Lambert Problem Solver

    Hi, asbjos re: education/occupation. As you might have guessed, I have some background in maths and physics. However, for most of my professional life, I've functioned as a business developer, commercial contract negotiator and a regulator. I have no academic affiliations. re: why am I...
  9. M

    A Lambert Problem Solver

    Lambert’s problem is concerned with the determination of an orbit from two position vectors - an initial point, \mathbf{R}_1; and a final point, \mathbf{R}_2 with radius r_1 and r_2, respectively; a known time-of-flight, \Delta T; and a central Keplerian gravitational field of known...
  10. M

    Changing the argument of periapsis - two-burn solution

    Hi, Vasco - I doubt that the transfer strategy is truly optimal, although I suspect that it is 'close' to being an optimal two-burn solution. The advantage of the proposed solution is that it is relatively straightforward to implement in Orbiter. The way to check optimality would be to set up...
  11. M

    Solar radiation pressure rotation matrix

    I can probably help. But it’s Christmas and I’m traveling over the next few days. I’ll get back to you on this.
  12. M

    From BCI to BCBF and back again

    This is a quick update on the my preceding posts in this thread. Of late, I've been going though a process and updating a number of coordinate transformations so that they are based on quaternion multiplications rather than rotation matrices - see, for example, Quaternions, rotations and...
  13. M

    Can I get the Vector components xyz given only this information?

    This is a short follow-up from earlier posts in this thread. In post #8, I outlined a method for calculating the radial and transverse components of the initial and final velocity vectors of the Keplerian arc connecting the initial and final points, \mathbf{R}_i and \mathbf{R}_f. from this...
  14. M

    Quaternions, rotations and orbital elements

    That may indeed be the case. However, I just think quaternions are interesting.
  15. M

    Quaternions, rotations and orbital elements

    This is a short (but somewhat technical note) on the rather arcane subject of converting a point in the perifocal reference frame to a more general x-y-z reference frame using quaternions. To get the ball rolling, let's introduce the perifocal reference frame. The perifocal reference frame...
  16. M

    Can I get the Vector components xyz given only this information?

    Actually, it occurs to me that the solution to ncc1701d's original problem is actually quite trivial - given that we are given the time of flight on each of the arc segments (120 seconds each). This means that the information about speeds is superfluous and one just needs to use a standard...
  17. M

    Can I get the Vector components xyz given only this information?

    I'm a bit suspicious of the orbital speeds given in the opening post, but here is the general procedure for solving this problem for Keplerian orbits where the points are separated by less than half an orbit: Let's suppose, as above, that you are given two (3-vector) points on an Keplerian...
  18. M

    Calculate (not derive) Orbital Velocity Vector

    To convert the 2d vector to a 3d vector (relative to the coordinate system of a parent body), one needs 'rotate' to the x-y-z reference frame of the parent body from the natural, perifocal reference frame of the elliptical/hyperbolic orbit. This rotation is defined in terms of three angles...
  19. M

    Challenge LOP-G to Brighton Beach and Back Again

    I'm really quite impressed with what you've managed to achieve here with GMAT. The dV numbers that you quote make intuitive sense: if one thinks of a NRHO as glorified highly eccentric Keplerian orbit (albeit one subject to string tidal forces from the Earth), the periapsis speed needed to...
  20. M

    Challenge LOP-G to Brighton Beach and Back Again

    Yes, I agree. Orbiter isn't well equipped for dealing with these orbits given the readily available tool set. Using GMAT sounds promising, though. Rendezvous at apoapsis would have astronauts in the lunar lander for three-four days. Let's hope that whatever design for the lunar lander is...