Axes

add_axes!(fs::FrameSystem{O, T}, ax::FrameAxesNode{O, T}) where {O,T}

Add axes to the frame system.

add_axes!(frames, name::Symbol, id::Int, class::Int, funs, parentid)

Add a new axes node to frames.

Inputs

• frames – Target frame system
• name – Axes name, must be unique within frames
• id – Axes ID, must be unique within frames
• funs – FrameAxesFunctions object storing the functions to compute the DCM and, eventually, its time derivatives.
• parentid – Axes ID of the parent axes. Not required only for the root axes.

add_axes_fixedoffset!(frames, name::Symbol, id::Int, parent, dcm:DCM)

Add axes name with id id to frames with a fixed-offset from parent. Fixed offset axes have a constant orientation with respect to their parent axes, represented by dcm, a Direction Cosine Matrix (DCM).

See also

See also add_axes!.

add_axes_projected!(frames, name, id, parent, fun)

Add inertial axes name and id id as a set of projected axes to frames. The axes relation to the parent axes are given by a fun.

Projected axes are similar to rotating axis, except that all the positions, velocity, etc ... are rotated by the 0-order rotation (i.e. the derivatives of the rotation matrix are null, despite the rotation depends on time).

See also

See also add_axes!.

add_axes_rotating!(frames, name::Symbol, id::Int, parent, fun, δfun=nothing, 
    δ²fun=nothing, δ³fun=nothing)

Add axes as a set of rotating axes to frames. The orientation of these axes depends only on time and is computed through the custom functions provided by the user.

The input functions must accept only time as argument and their outputs must be as follows:

• fun: return a Direction Cosine Matrix (DCM).
• δfun: return the DCM and its 1st order time derivative.
• δ²fun: return the DCM and its 1st and 2nd order time derivatives.
• δ³fun: return the DCM and its 1st, 2nd and 3rd order time derivatives.

If δfun, δ²fun or δ³fun are not provided, they are computed via automatic differentiation.

add_axes_alias!(frames, target, alias::Symbol)

Add a name alias to a target axes registered in frames.

add_axes_ephemeris!(frames::FrameSystem{O, T}, eph::AbstractEphemerisProvider, 
    name::Symbol, id::Int, seq::Symbol) where {O, T}

Add axes coming from an AbstractEphemerisProvider subtype to frames. The axes are identifies by the id and a have a user defined name. The rotation matrix is build using the rotation sequence specified in seq. The axes type is specified by class.

add_axes_gcrf!(frames::FrameSystem)

Add the Geocentric Celestial Reference Frame (GCRF) to the frames graph. The axes are automatically named GCRF and assigned the 23 ID. These axes can only be defined as a set of root axes or as child of the ICRF (ID = 1).

See also

See also add_axes_icrf! and AXESID_GCRF.

add_axes_icrf!(frames::FrameSystem)

Add the International Celestial Reference Frame (ICRF) as the root axes of the frames graph. The axes are automatically named ICRF and assigned the 1 ID.

See also

See also add_axes!, add_axes_gcrf! and AXESID_ICRF.

add_axes_eme2000!(frames, name::Symbol=:EME2000, parentid::Int=AXESID_ICRF, 
    id::Int = AXESID_EME2000)

Add Mean Equator Mean Equinox of J2000 axes to frames. Custom name, id and parentid can be assigned by the user.

See also

See also DCM_ICRF_TO_EME2000.

add_axes_ecl2000!(frames, name::Symbol=:ECL2000, parentid::Int, id::Int = AXESID_ECL2000; 
    model::IERSModel=iers1996)

Add Ecliptic Equinox of J2000 (ECL2000) axes to frames. Custom id, name and parentid can be assigned by the user. The admissible parent axes are the following:

• ICRF: for the International Celestial Reference Frame, with ID = 1
• GCRF: for the Geocentric Celestial Reference Frame, with ID = 23
• EME2000: the Mean Earth/Moon Ephemeris of J2000, with ID = 22

add_axes_itrf!(fr::FrameSystem, name::Symbol, parentid::Int=AXESID_ICRF, id::Int=AXESID_ITRF,
    model::IERSModel=iers2010b)

Add International Terrestrial Reference Frame (ITRF) axes to fr. Use the model argument to specify which IERS convention should be used for the computations.

add_axes_tirf!(fr::FrameSystem, name::Symbol, id::Int, parentid::Int=AXESID_ICRF, 
    model::IERSModel=iers2010b)

Add Terrestrial Intermediate Reference Frame (TIRF) axes to fr. Use the model argument to specify which IERS convention should be used for the computations.

add_axes_cirf!(fr::FrameSystem, name::Symbol, id::Int, parentid::Int=AXESID_ICRF, 
    model::IERSModel=iers2010b)

Add Celestial Intermediate Reference Frame (CIRF) axes to fr. Use the model argument to specify which IERS convention should be used for the computations.

add_axes_mod!(fr, name::Symbol, axesid::Int, parentid::Int, 
    model::IERSConventions.IERSModel=iers2010b)

Add Mean Equator and Equinox of Date (MOD) axes to fr. Use the model argument to specify which IERS convention should be used for the computations.

add_axes_tod!(fr::FrameSystem, name::Symbol, id::Int, parentid::Int=AXESID_ICRF, 
    model::IERSModel=iers2010b)

Add True Equator of Date (TOD) axes to fr. Use the model argument to specify which IERS convention should be used for the computations.

add_axes_gtod!(fr::FrameSystem, name::Symbol, id::Int, parentid::Int=AXESID_ICRF, 
    model::IERSModel=iers2010b)

Add Greenwich True-of-Date (GTOD) axes to fr. Use the model argument to specify which IERS convention should be used for the computations.

add_axes_pef!(fr::FrameSystem, name::Symbol, id::Int, parentid::Int=AXESID_ICRF, 
    model::IERSModel=iers2010b)

Add Pseudo-Earth Fixed (PEF) axes to fr. Use the model argument to specify which IERS convention should be used for the computations.

add_axes_bci2000!(fr, axes::AbstractFrameAxes, center, data)

Add Body-Centered Inertial (BCI) axes at J2000 with name and id to fr. The center point (i.e., the reference body) is center.

See also

See also add_axes_fixedoffset!, add_axes_bcrtod!.

add_axes_bcrtod!(fr, name, id, center; deriv=true)

Add Body-Centered Rotating (BCR), True-of-Date (TOD) axes with name and id to fr. The center point (i.e., the reference body) is center.

These axes are the equivalent of SPICE's IAU_<BODY_NAME> frames.

See also

See also add_axes_rotating!, add_axes_bci2000!.

add_axes_me421!(frames, name::Symbol, parentid::Int, axesid::Int=AXESID_MOONME_DE421)

Add DE421 Moon's Mean Earth/Mean Rotation (ME) axes to frames.

add_axes_pa421!(frames, eph::AbstractEphemerisProvider, name::Symbol, 
    id::Int=AXESID_MOONPA_DE421)

Add DE421 Moon's Principal Axes (PA) axes to frames. The libration angles are extracted from the eph ephemeris kernels, an error is thrown if such orientation data is not available.

add_axes_pa440!(frames, eph::AbstractEphemerisProvider, name::Symbol, 
    id::Int=AXESID_MOONPA_DE440)

Add DE440 Moon's Principal Axes (PA) axes to frames. The libration angles are extracted from the eph ephemeris kernels, an error is thrown if such orientation data is not available.

add_axes_topocentric!(frames, name::Symbol, id::Int, parent, λ, ϕ, mount)

Add topocentric axes to frames at a specified location and mounting.

The orientation relative to the parent axes parent is defined throuh the longitude λ, the geodetic latitude ϕ and the mounting type mount, which may be any of the following:

• :NED (North, East, Down): the X-axis points North, the Y-axis is directed eastward and the Z-axis points inwards towards the nadir.
• :SEZ (South, East, Zenith): the X-axis points South, the Y-axis is directed East, and the Z-axis points outwards towards the zenith.
• :ENU (East, North, Up): the X-axis points East, the Y-axis is directed North and the Z-axis points outwards towards the zenith.

function add_axes_twodir!(frames::FrameSystem{O,T}, name::Symbol, id, parent, 
    dir1::Symbol, dir2::Symbol, seq::Symbol; project::Bool=false) where {O,T}

Add a set of axes to frames based on two directions.

A right-handed coordinate system is generated based on the specified sequence direction (seq), which determines the order in which the vectors are used to define the basis. The project flag specifies whether the resulting axes are inertial or not.

See also

See also add_axes_projected! and add_axes_rotating!.

add_axes_frozen!(fr, name, id, frozen, e)

Create a frozen axes version of frozen at epoch e, with name and id and add it to frames.

add_axes_fixed_quaternion!(frames::FrameSystem, name::Symbol, id::Int, parent, q::Quaternion)

Add axes name with id id to frames with a fixed-offset from parent. Fixed offset axes have a constant orientation with respect to their parent axes, represented by the quaternion q.

See also

See also add_axes_fixedoffset!.

add_axes_fixed_angles!(frames, name::Symbol, id::Int, parent, θ::AbstractVector{N}, seq::Symbol)

Add axes name with id id to frames with a fixed-offset from parent. Fixed offset axes have a constant orientation with respect to their parent axes, represented by Euler angles θ.

The rotation sequence is defined by seq specifing the rotation axes. The possible values depends on the number of rotations as follows:

• 1 rotation (θ₁): :X, :Y, or :Z.
• 2 rotations (θ₁, θ₂): :XY, :XZ, :YX, :YZ, :ZX, or :ZY.
• 3 rotations (θ₁, θ₂, θ₃): :XYX, XYZ, :XZX, :XZY, :YXY, :YXZ, :YZX, :YZY, :ZXY, :ZXZ, :ZYX, or :ZYZ

See also

See also add_axes_fixedoffset!.

add_axes_fixed_angleaxis!(frames, name::Symbol, id::Int, parent, ϕ::Number, v::AbstractVector{N})

Add axes name with id id to frames with a fixed-offset from parent. Fixed offset axes have a constant orientation with respect to their parent axes, represented by Euler angle ϕ [rad] and Euler axis v.

See also

See also add_axes_fixedoffset!.

AXESID_ICRF

NAIF Axes ID for the International Celestial Reference Frame (ICRF).

AXESID_MOONME_DE421

NAIF axes id for the DE421 Moon Mean Earth/Mean Rotation axes (ME421).

AXESID_MOONPA_DE421

NAIF axes id for the DE421 Moon Principal Axes (PA421).

AXESID_MOONPA_DE440

NAIF Axes id for the DE440 Moon Principal Axes (PA440).

AXESID_ECL2000

NAIF Axes ID for the Mean Ecliptic Equinox of J2000 (ECL2000).

AXESID_EME2000

Axes ID for the Mean Dynamical Equator and Equinox of J2000.0.

AXESID_GCRF

Axes ID for the Geocentric Celestial Reference Frame (GCRFF)

DCM_ICRF_TO_EME2000

DCM for the rotation from the International Celestial Reference Frame (ICRF) and the Mean Equator and Equinox of J2000.0 (EME2000). This corresponds to the J2000 frame in the SPICE toolkit.

References

• Hilton, James L., and Catherine Y. Hohenkerk. – Rotation matrix from the mean dynamical equator and equinox at J2000. 0 to the ICRS. – Astronomy & Astrophysics 513.2 (2004): 765-770. DOI: 10.1051/0004-6361:20031552
• SOFA docs