Recent content by MontBlanc2012

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    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
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    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.)...
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    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...
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    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...
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    calculating relative inclination

    Yes, this is the correct expression for the relative inclination.
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    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...
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    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...
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    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...
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    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...
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    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...
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    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.
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    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...
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    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...
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    Quaternions, rotations and orbital elements

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