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‎docs/src/Examples/gen/.gitignore‎

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‎docs/src/Examples/gen/e01_cr3bp.jl‎

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using FrameTransformations
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CR3BP = FrameSystem{2, Float64}()
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add_axes_root!(CR3BP, :InertialAx, 1)
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add_point_root!(CR3BP, :EMBc, 1, 1)
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using ReferenceFrameRotations
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f(t) = angle_to_dcm(t, :Z)
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add_axes_rotating!(CR3BP, :SynodicAx, 2, 1, f)
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# This file was generated using Literate.jl, https://github.com/fredrikekre/Literate.jl

‎docs/src/Examples/gen/e01_cr3bp.md‎

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```@meta
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EditURL = "../e01_cr3bp.jl"
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```
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# [Use Case: CR3BP](@id example_01_cr3bp)
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_This example was generated on 2024-05-31T10:00:28.409._
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The power of the [`FrameSystem`](@ref) is its capability to handle axes
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transformations and point translations of both high-accuracy and simplified
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models. The use-case here presented includes the case of the Circular-Restricted
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Three-Body Problem (CR3BP) rotating frame transformation handling.
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In particular, when dealing with the [CR3BP](https://orbital-mechanics.space/the-n-body-problem/circular-restricted-three-body-problem.html),
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mission analysis are used to exploit non-dimensional, rotating coordinates
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to express the equations of motion and perform the computations.
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In this tutorial, we create a [`FrameSystem`](@ref) to handle transformations
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within the Earth-Moon CR3BP, which is characterized by a mass ratio of
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approximately `μ = 0.012`. We start off by creating a frame system without any
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ephemeris provider, since we are using a simplified model.
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````@example e01_cr3bp
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using FrameTransformations
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CR3BP = FrameSystem{2, Float64}()
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````
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As always, the first step requires the definition of the root axes and points.
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In this case, we use the a generic set of _inertial axes_ and the Earth-Moon
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Barycenter (EMB).
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````@example e01_cr3bp
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add_axes_root!(CR3BP, :InertialAx, 1)
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add_point_root!(CR3BP, :EMBc, 1, 1)
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````
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We now proceed to add our synodic axes: in the CR3BP these are uniformly
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rotating with respect to the `InertialAx` about the Z-axis. Therefore, we
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leverage rotating axes.
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````@example e01_cr3bp
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using ReferenceFrameRotations
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f(t) = angle_to_dcm(t, :Z)
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add_axes_rotating!(CR3BP, :SynodicAx, 2, 1, f)
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````
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Note that there is no need to specify the rotation derivatives, as they'll
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be computed by automatic differentiation via the
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[ForwardDiff](https://github.com/JuliaSpaceMissionDesign/Ephemerides.jl) package.
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For performace-critical transformations, however, it is reccomended to manually
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define these derivatives.
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---
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*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*
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‎docs/src/Examples/gen/e02_hifi.jl‎

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using FrameTransformations
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using Ephemerides
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using LinearAlgebra
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using ReferenceFrameRotations
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url_pck = "https://naif.jpl.nasa.gov/pub/naif/generic_kernels/pck/moon_pa_de421_1900-2050.bpc";
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url_spk = "https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/planets/de432s.bsp";
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EPH = EphemerisProvider([download(url_spk), download(url_pck)])
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FRAMES = FrameSystem{3, Float64}()
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add_axes_icrf!(FRAMES)
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add_point_root!(FRAMES, :SSB, 0, 1)
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add_point_ephemeris!(FRAMES, EPH, :EMB, 3)
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add_point_ephemeris!(FRAMES, EPH, :Sun, 10)
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add_point_ephemeris!(FRAMES, EPH, :Earth, 399)
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add_point_ephemeris!(FRAMES, EPH, :Moon, 301)
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# This file was generated using Literate.jl, https://github.com/fredrikekre/Literate.jl

‎docs/src/Examples/gen/e02_hifi.md‎

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```@meta
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EditURL = "../e02_hifi.jl"
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```
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# [Use Case: High Fidelity](@id example_02_hifi)
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_This example was generated on 2024-05-31T10:00:28.413._
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Once the general structure of the [`FrameSystem`](@ref) is understood, we can pass to
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a use case in which we want to build and exploit our frame system to perform computations
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in a high-fidelity environment.
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### Frame system setup
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In this example, we plan on using ephemeris data to retrieve accurate positions
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of the planets and the orientation of certain reference frames. Therefore, we
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create an ephemeris provider object leveraging our own
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[`Ephemerides.jl`](https://github.com/JuliaSpaceMissionDesign/Ephemerides.jl) package
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and use it to generate a frame system instance:
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````@example e02_hifi
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using FrameTransformations
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using Ephemerides
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using LinearAlgebra
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using ReferenceFrameRotations
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url_pck = "https://naif.jpl.nasa.gov/pub/naif/generic_kernels/pck/moon_pa_de421_1900-2050.bpc";
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url_spk = "https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/planets/de432s.bsp";
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EPH = EphemerisProvider([download(url_spk), download(url_pck)])
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FRAMES = FrameSystem{3, Float64}()
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````
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Once the graph is created, we assign the `ICRF` (International Celestial Reference
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Frame) as our set of inertial root-axes:
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````@example e02_hifi
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add_axes_icrf!(FRAMES)
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````
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These axes are practically coincident with the `GCRF`.
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In this scenario, we will be working within the Cislunar environment, therefore
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we will need the major bodies that influence this dynamic regime, i..e, the Earth,
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the Moon and the Sun. To do so, we also define the Solar System Barycenter (SSB) and
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the Earth-Moon Barycenter (EMB) as the ephemeris data of the remaining bodies is
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expressed with respect to those.
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For this example, we will assume the SSB is our root point:
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````@example e02_hifi
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add_point_root!(FRAMES, :SSB, 0, 1)
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add_point_ephemeris!(FRAMES, EPH, :EMB, 3)
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add_point_ephemeris!(FRAMES, EPH, :Sun, 10)
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add_point_ephemeris!(FRAMES, EPH, :Earth, 399)
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add_point_ephemeris!(FRAMES, EPH, :Moon, 301)
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````
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---
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*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*
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‎docs/src/Examples/gen/e03_customorb.jl‎

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using FrameTransformations
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G = FrameSystem{4, Float64}()
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add_axes_icrf!(G)
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add_point_root!(G, :Earth, 399, 1)
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using JSMDInterfaces.Math: interpolate
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using JSMDUtils.Math: InterpCubicSplines
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c = 2π/86400
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de = 0:3600:2*86400;
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fv(t) = [cos(c*t), sin(c*t), 0, -c*sin(c*t), c*cos(c*t), 0];
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fv2(t) = [sin(c*t), cos(c*t), 0];
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const ORB1 = InterpCubicSplines(de, hcat([fv(e) for e in de]...));
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const ORB2 = InterpCubicSplines(de, hcat([fv2(e) for e in de]...));
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add_point_dynamical!(G, :SC1, -1, 399, 1, t->interpolate(ORB1, t)[1:3], t->interpolate(ORB1, t))
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add_point_dynamical!(G, :SC2, -2, 399, 1, t->interpolate(ORB2, t))
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vector12(G, 399, -1, 1, 12345.0)
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vector12(G, -1, -2, 1, 12345.0)
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# This file was generated using Literate.jl, https://github.com/fredrikekre/Literate.jl

‎docs/src/Examples/gen/e03_customorb.md‎

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```@meta
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EditURL = "../e03_customorb.jl"
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```
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# [Use Case: Custom spacecraft orbit](@id example_03_orb)
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_This example was generated on 2024-05-31T10:00:28.419._
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Once the general structure of the [`FrameSystem`](@ref) is understood, we can pass to
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a use case in which we want to build and exploit our frame system to perform computations
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inserting a custom orbit. This becomes especially crucial in complex cases like Trajectory
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Optimization and Navigation Analysis.
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In such scenarios, the trajectory is under design, and the trajectory information might
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not be completely available. Moreover, in these cases derivatives could be required for
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various quantities such as time, states, and parameters.
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In this context, we shall remember that `FrameTransformations` is able to perform operations,
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including AD, on the frames **independent variable**, e.g. only time.
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A proper orbit representation is essential to avoid perturbation confusion and ensure
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proper custom orbit handling. For this purpose, two point types can seems suitable:
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`updatable` and `dynamical` points.
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In this case, however, `updatable` points are not well-suited as they are essentially
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constants for the AD system. Then, `dynamical` points can effectively handle this scenario.
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### Frame system setup
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First of all, a new [`FrameSystem`](@ref) shall be created.
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````@example e03_customorb
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using FrameTransformations
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G = FrameSystem{4, Float64}()
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add_axes_icrf!(G)
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add_point_root!(G, :Earth, 399, 1)
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````
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!!! note
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As the orbit considered in this example is custom, there is no requirement
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to load ephemeris.
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### Custom orbit model
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A custom orbit model is then required. In this case two dummy orbits are
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created and stored in a `CubicSpline` object.
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````@example e03_customorb
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using JSMDInterfaces.Math: interpolate
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using JSMDUtils.Math: InterpCubicSplines
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c = 2π/86400
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de = 0:3600:2*86400;
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fv(t) = [cos(c*t), sin(c*t), 0, -c*sin(c*t), c*cos(c*t), 0];
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fv2(t) = [sin(c*t), cos(c*t), 0];
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const ORB1 = InterpCubicSplines(de, hcat([fv(e) for e in de]...));
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const ORB2 = InterpCubicSplines(de, hcat([fv2(e) for e in de]...));
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nothing #hide
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````
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### Custom orbit handling
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Given the custom orbit model, [`add_point_dynamical!`](@ref) could be used
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to link it to the frame system.
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Insert dynamical points
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````@example e03_customorb
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add_point_dynamical!(G, :SC1, -1, 399, 1, t->interpolate(ORB1, t)[1:3], t->interpolate(ORB1, t))
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add_point_dynamical!(G, :SC2, -2, 399, 1, t->interpolate(ORB2, t))
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````
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Once in the frame system, AD could be exploited to retrieve states+gradients w.r.t.
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time in any registered frame:
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````@example e03_customorb
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vector12(G, 399, -1, 1, 12345.0)
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````
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It is also possible to use the computational graph to compute quantities between
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completely custom states representations:
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````@example e03_customorb
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vector12(G, -1, -2, 1, 12345.0)
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````
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---
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*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*
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‎docs/src/Tutorials/gen/.gitignore‎

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‎docs/src/Tutorials/gen/t00_frames.jl‎

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using FrameTransformations
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using Tempo
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F = FrameSystem{2, Float64}()
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F = FrameSystem{2, Float64, InternationalAtomicTime}()
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has_point(F, 1)
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has_axes(F, 1)
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has_direction(F, :Root)
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axes(F)
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points(F)
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order(F)
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FrameTransformations.timescale(F)
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using Ephemerides, Downloads
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url = "https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/planets/a_old_versions/de421.bsp";
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eph = EphemerisProvider(Downloads.download(url));
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F = FrameSystem{2, Float64}()
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add_axes_icrf!(F)
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add_point_root!(F, :SSB, 0, 1)
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add_point_ephemeris!(F, eph, :Sun, 10)
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add_point_ephemeris!(F, eph, :EMB, 3)
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# This file was generated using Literate.jl, https://github.com/fredrikekre/Literate.jl

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