GitHub

Library

Documentation for AstroCoords.jl.

AstroCoords.AstroCoordTransformation — Type
abstract type AstroCoordTransformation <: AstrodynamicsTransformation

An abstract type representing a Transformation Between Astrodynamics Coordinates with no Time Regularization

source
AstroCoords.Cartesian — Type
Cartesian{T} <: AstroCoord

Cartesian Orbital Elements. 6D parameterziation of the orbit. x - X-position y - Y-position z - Z-position ẋ - X-velocity ẏ - Y-velocity ż - Z-velocity

Constructors Cartesian(x, y, z, ẋ, ẏ, ż) Cartesian(X::AbstractArray) Cartesian(X::AstroCoord, μ::Number)

source
AstroCoords.Coordinate — Type
abstract type AstroCoord{N, T} <: StaticMatrix{N, 1, T}

An abstract type representing a N-Dimensional Coordinate Set

source
AstroCoords.Cylindrical — Type
Cylindrical{T} <: AstroCoord

Cylindrical Orbital Elements. 6D parameterziation of the orbit ρ - in-plane radius θ - in-plane angle z - out-of-plane distance ρdot - instantaneous rate of change of in-plsne radius θdot - instantaneous rate of change of θ ż - instantaneous rate of change of z

Constructors Cylindrical(r, θ, z, ṙ, θdot, ż) Cylindrical(X::AbstractArray) Cylindrical(X::AstroCoord, μ::Number)

source
AstroCoords.Delaunay — Type
Delaunay{T} <: AstroCoord

Delaunay Orbital Elements. 6D parameterziation of the orbit. L - Canonical Keplerian Energy G - Canonical Total Angular Momentum H - Canonical Normal Angular Momentum (Relative to Equator) M - Mean Anomaly ω - Argument of Periapsis Ω - Right Ascention of the Ascending Node

Constructors Delaunay(L, G, H, M, ω, Ω) Delaunay(X::AbstractVector{<:Number}) Delaunay(X::AstroCoord, μ::Number)

source
AstroCoords.Keplerian — Type
Keplerian{T} <: AstroCoord

Keplerian Orbital Elements. 6D parameterziation of the orbit. a - semi-major axis e - eccetricity i - inclination Ω - Right Ascension of Ascending Node ω - Argument of Perigee f - True Anomaly

Constructors Keplerian(a, e, i, Ω, ω, f) Keplerian(X::AbstractArray) Keplerian(X::AstroCoord, μ::Number)

source
AstroCoords.Milankovich — Type
Milankovich{T} <: AstroCoord

Milankovich Orbital Elements. 7D parameterziation of the orbit. hx - X-component of Angular Momentum Vector hy - Y-component of Angular Momentum Vector hz - Z-component of Angular Momentum Vector ex - X-component of Eccentricity Vector ey - Y-component of Eccentricity Vector ez - Z-component of Eccentricity Vector L - Mean Anomaly

Constructors Milankovich(hx, hy, hz, ex, ey, ez, L) Milankovich(X::AbstractArray) Milankovich(X::AstroCoord, μ::Number)

source
AstroCoords.ModEq — Type
ModEq{T} <: AstroCoord

Modified Equinoctial Orbital Elements. 6D parameterziation of the orbit. p - f - g - h - k - L -

Constructors ModEq(p, f, g, h, k, l) ModEq(X::AbstractArray) ModEq(X::AstroCoord, μ::Number)

source
AstroCoords.Spherical — Type
Spherical{T} <: AstroCoord

Spherical Orbital Elements. 6D parameterziation of the orbit r - radius θ - in-plane angle ϕ - out-of-plane angle ṙ - instantaneous rate of change of radius θdot - instantaneous rate of change of θ ϕdot - instantaneous rate of change of ϕ

Constructors Spherical(r, θ, ϕ, ṙ, ω, Ω) Spherical(X::AbstractArray) Spherical(X::AstroCoord, μ::Number)

source
AstroCoords.Transformation — Type

The Transformation supertype defines a simple interface for performing transformations. Subtypes should be able to apply a coordinate system transformation on the correct data types by overloading the call method, and usually would have the corresponding inverse transformation defined by Base.inv(). Efficient compositions can optionally be defined by compose() (equivalently ∘).

source
AstroCoords.USM6 — Type
USM6{T} <: AstroCoord

Unified State Model Orbital Elements. 6D parameterziation of the orbit using Velocity Hodograph and MRP's C - Velocity Hodograph Component Normal to the Radial Vector Laying in the Orbital Plane Rf1 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame X-Axis Rf2 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame Y-Axis σ1 - First Modified Rodriguez Parameter σ2 - Second Modified Rodriguez Parameter σ3 - Third Modified Rodriguez Parameter

Constructors USM6(C, Rf1, Rf2, σ1, σ2, σ3) USM6(X::AbstractArray) USM6(X::AstroCoord, μ::Number)

source
AstroCoords.USM7 — Type
USM7{T} <: AstroCoord

Unified State Model Orbital Elements. 7D parameterziation of the orbit using Velocity Hodograph and Quaternions C - Velocity Hodograph Component Normal to the Radial Vector Laying in the Orbital Plane Rf1 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame X-Axis Rf2 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame Y-Axis ϵO1 - First Imaginary Quaternion Component ϵO2 - Second Imaginary Quaternion Component ϵO3 - Third Imaginary Quaternion Component η0 - Real Quaternion Component

Constructors USM7(C, Rf1, Rf2, ϵO1, ϵO2, ϵO3, η0) USM7(X::AbstractArray) USM7(X::AstroCoord, μ::Number)

source
AstroCoords.USMEM — Type
USMEM{T} <: AstroCoord

Unified State Model Orbital Elements. 6D parameterziation of the orbit using Velocity Hodograph and Exponential Mapping C - Velocity Hodograph Component Normal to the Radial Vector Laying in the Orbital Plane Rf1 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame X-Axis Rf2 - Velocity Hodograph Component 90 degrees ahead of the Eccentricity Vector - Along the Intermediate Rotating Frame Y-Axis a1 - First Exponential Mapping Component a2 - First Exponential Mapping Component a3 - First Exponential Mapping Component

Constructors USMEM(C, Rf1, Rf2, a1, a2, a3) USMEM(X::AbstractArray) USMEM(X::AstroCoord, μ::Number)

source
AstroCoords.KeplerSolver — Method

Solves for True Anomaly given the Mean Anomaly and eccentricity of an Orbit

Arguments: -'M::Number': Mean Anomaly of the orbit -'e::Number': Eccentricity of the orbit

Returns -'f::Number': True Anomaly of the orbit *All angles are in radians

source
AstroCoords.Mil2cart — Method

Mil2cart(u::AbstractVector{<:Number}, μ::Number)

Converts Milankovich State Vector into the Cartesian State

Arguments: -'u::AbstractVector{<:Number}': Milankovich State Vector [H; e; L] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_cart::Vector{<:Number}': Cartesian State Vector [x; y; z; ẋ; ẏ; ż]

source
AstroCoords.ModEq2koe — Method
ModEq2koe(u::AbstractVector{<:Number}, μ::Number)

Converts Modified Equinoctial Elements into the Keplerian Elements

Arguments: -'u:AbstractVector{<:Number}': Modified Equinoctial State Vector [p; f; g; h; k; l] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_koe::Vector{<:Number}': Keplerian State Vector [a; e; i; Ω(RAAN); ω(AOP); ν(True Anomaly)] *All Angles are in Radians

source
AstroCoords.ModEqN2koe — Method
ModEqN2koe(u::AbstractVector{<:Number}, μ::Number)

Converts Modified Equinoctial Elements with Mean Motion into the Keplerian Elements

Arguments: -'u:AbstractVector{<:Number}': Modified Equinoctial State Vector [p; f; g; h; k; l] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_koe::Vector{<:Number}': Keplerian State Vector [a; e; i; Ω(RAAN); ω(AOP); ν(True Anomaly)] *All Angles are in Radians

source
AstroCoords.USM62USM7 — Method
USM62USM7(u::AbstractArray{<:Number}, μ::Number)

Converts USM with Modified Rodrigue Parameters to USM with Quaternions

Arguments: -'u::AbstractVector{<:Number}': USM6 Vector [C; Rf1; Rf2; σ1; σ2; σ3] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_USM::Vector{Number}': Unified State Model Vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0]

source
AstroCoords.USM72USM6 — Method
USM72USM6(u::AbstractVector{<:Number}, μ::Number)

Converts USM with Quaternions to USM with Modified Rodrigue Parameters

Arguments: -'u::AbstractVector{<:Number}': Unified State Model Vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_USM6::Vector{Number}': USM6 State Vector [C; Rf1; Rf2; σ1; σ2; σ3]

source
AstroCoords.USM72USMEM — Method
USM72USMEM(u::AbstractVector{<:Number}, μ::Number)

Converts USM with Quaternions to USM with Exponential Mapping

Arguments: -'u::AbstractVector{<:Number}': Unified State Model Vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_USMEM::Vector{Number}': USMEM State Vector [C; Rf1; Rf2; a1; a2; a3, Φ]

source
AstroCoords.USM72koe — Method
USM72koe(u::AbstractVector{<:Number}, μ::Number)

Converts Unified State Model elements into the Keplerian Orbital Element Set Van den Broeck, Michael. "An Approach to Generalizing Taylor Series Integration for Low-Thrust Trajectories." (2017). https://repository.tudelft.nl/islandora/object/uuid%3A2567c152-ab56-4323-bcfa-b076343664f9

Arguments: -'u::AbstractVector{<:Number}': Unified State Model Vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_koe:Vector{<:Number}': Keplerian State Vector [a; e; i; Ω(RAAN); ω(AOP); f(True Anomaly)] *All Angles are in Radians

source
AstroCoords.USMEM2USM7 — Method
USMEM2USM7(u::AbstractVector{<:Number}, μ::Number)

Converts USM with Exponential Mapping to USM with Quaternions

Arguments: -'u::AbstractVector{<:Number}': USMEM Vector [C; Rf1; Rf2; a1; a2; a3, Φ] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_USM::Vector{<:Number}': Unified State Model Vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0]

source
AstroCoords.angularMomentumQuantity — Method

Computes the Instantaneous Angular Velocity Quantity

Arguments: -'u::AbstractVector{<:Number}': Cartesian State Vector [x; y; z; ẋ; ẏ; ż]

Returns -'angular_momentum::Number' - Norm of Angular Momentum Vector

source
AstroCoords.angularMomentumQuantity — Method

Computes the Instantaneous Angular Velocity Quantity

Arguments: -'X::AstroCoord': Astro Coordinate -'μ::Number': Standard Graviational Parameter of Central Body

Returns -'angular_momentum::Number' - Norm of Angular Momentum Vector

source
AstroCoords.angularMomentumVector — Method

Computes the Instantaneous Angular Velocity Vector

Arguments: -'u::AbstractVector{<:Number}': Cartesian State Vector [x; y; z; ẋ; ẏ; ż]

Returns -'angular_momentum::Vector{<:Number}' - 3-Dimensional Angular Momemtum Vector

source
AstroCoords.angularMomentumVector — Method

Computes the Instantaneous Angular Velocity Vector

Arguments: -'X::AstroCoord': Astro Coordinate -'μ::Number': Standard Graviational Parameter of Central Body

Returns -'angular_momentum::Vector{<:Number}' - 3-Dimensional Angular Momemtum Vector

source
AstroCoords.cart2Mil — Method
cart2Mil(u::AbstractVector{<:Number}, μ::Number)

Converts Cartesian State Vector into the Milankovich State

Arguments: -'u::AbstractVector{<:Number}': Cartesian State Vector [x; y; z; ẋ; ẏ; ż] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_Mil::Vector{Number}': Milankovich State Vector [H; e; L]

source
AstroCoords.cart2cylind — Method

cart2cylind(u::AbstractVector{<:Number}, μ::Number)

Computes the Cylindrical Orbital Elements from a Cartesian Set

Arguments: -'u::AbstractVector{<:Number}': Cartesian State Vector [x; y; z; ẋ; ẏ; ż] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_cylind::Vector{<:Number}': Cylindrical Orbital Element Vector [r; θ; z; ṙ; θdot; ż] *All Angles are in Radians

source
AstroCoords.cart2delaunay — Method
cart2delaunay(u::AbstractVector{<:Number}, μ::Number)

Computes the Delaunay Orbital Elements from a Cartesian Set

Arguments: -'u::AbstractVector{<:Number}': Cartesian Orbital Element Vector [x; y; z; ẋ; ẏ; ż] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_cart::Vector{<:Number}': Delaunay Orbital Element Vector [L; G; H; M; ω; Ω] *All Angles are in Radians

source
AstroCoords.cart2koe — Method
cart2koe(u::AbstractVector{T}, μ::Number; equatorial_tol::Float64=1E-15, circular_tol::Float64=1E-15)

Computes the Keplerian Orbital Elements from a Cartesian Set.

Arguments: -'u::AbstractVector{<:Number}': Cartesian State Vector [x; y; z; ẋ; ẏ; ż] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_koe::Vector{<:Number}': Keplerian Orbital Element Vector [a; e; i; Ω(RAAN); ω(AOP); f(True Anomaly)] *All Angles are in Radians

source
AstroCoords.cart2koeM — Method

Converts Cartesian State Vector into the Alternative Keplerian State Vector

Arguments: -'u::AbstractVector{<:Number}': Cartesian State Vector [x; y; z; ẋ; ẏ; ż] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_cart::Vector{<:Number}': Alternative Keplerian State Vector [a; e; i; Ω(RAAN); ω(AOP); M(Mean Anomaly)]

source
AstroCoords.cart2sphere — Method
cart2sphere(u::AbstractVector{<:Number}, μ::Number)

Computes the Spherical Orbital Elements from a Spherical Set

Arguments: -'u::AbstractVector{<:Number}': Cartesian State Vector [x; y; z; ẋ; ẏ; ż] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_sphere::Vector{<:Number}': Spherical Orbital Element Vector [r; θ; ϕ; ṙ; θdot; ϕdot] *All Angles are in Radians

source
AstroCoords.cylind2cart — Method
cylind2cart(u::AbstractVector{<:Number}, μ::Number)

Computes the Cartesian Orbital Elements from a Cylindrical Set

Arguments: -'u::AbstractVector{<:Number}': Cylindrical State Vector [r; θ; z; ṙ; θdot; ż] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_cart::Vector{<:Number}': Cartesian Orbital Element Vector [x; y; z; ẋ; ẏ; ż] *All Angles are in Radians

source
AstroCoords.delaunay2cart — Method
delaunay2cart(u::AbstractVector{<:Number}, μ::Number)

Computes the Cartesian Orbital Elements from a Delaunay Set Laskar, Jacques. "Andoyer construction for Hill and Delaunay variables." Celestial Mechanics and Dynamical Astronomy 128.4 (2017): 475-482.

Arguments: -'u::AbstractVector{<:Number}': Delaunay Orbital Element Vector [L; G; H; M; ω; Ω] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_cart::Vector{<:Number}': Cartesian Orbital Element Vector [x; y; z; ẋ; ẏ; ż] *All Angles are in Radians

source
AstroCoords.eccentricAnomaly2MeanAnomaly — Method

Converts the True Anomaly into the Mean Anomaly

Arguments: -'E::Number': Eccentric Anomaly of the orbit -'e::Number': Eccentricity of the orbit

Returns -'M::Number': Mean Anomaly of the orbit *All angles are in radians

source
AstroCoords.eccentricAnomaly2TrueAnomaly — Method

Converts the Eccentric Anomaly into the True Anomaly

Arguments: -'E::Number': Eccentric Anomaly of the orbit -'e::Number': Eccentricity of the orbit

Returns -'f::Number': True Anomaly of the orbit *All angles are in radians

source
AstroCoords.koe2ModEq — Method
koe2ModEq(u::AbstractVector{<:Number}, μ::Number)

Converts Keplerian Elements into the Modified Equinoctial Elements

Arguments: -'u:AbstractVector{<:Number}': Keplerian State Vector [a; e; i; Ω(RAAN); ω(AOP); ν(True Anomaly)] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_ModEq::Vector{<:Number}': Modified Equinoctial State Vector [p; f; g; h; k; l] *All Angles are in Radians

source
AstroCoords.koe2ModEqN — Method
koe2ModEqN(u::AbstractVector{<:Number}, μ::Number)

Converts Keplerian Elements into the Modified Equinoctial Elements with Mean Motion

Arguments: -'u:AbstractVector{<:Number}': Keplerian State Vector [a; e; i; Ω(RAAN); ω(AOP); ν(True Anomaly)] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_ModEq::Vector{<:Number}': Modified Equinoctial State Vector [n; f; g; h; k; l] *All Angles are in Radians

source
AstroCoords.koe2USM7 — Method
koe2USM7(u::AbstractVector{<:Number}, μ::Number)

Converts Keplerian Orbital Elements into the Unified State Model Set Van den Broeck, Michael. "An Approach to Generalizing Taylor Series Integration for Low-Thrust Trajectories." (2017). https://repository.tudelft.nl/islandora/object/uuid%3A2567c152-ab56-4323-bcfa-b076343664f9

Arguments: -'u:AbstractVector{<:Number}': Keplerian State Vector [a; e; i; Ω(RAAN); ω(AOP); f(True Anomaly)] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_USM::Vector{<:Number}': Unified State Model Vector [C; Rf1; Rf2; ϵO1; ϵO2; ϵO3; η0] *All Angles are in Radians

source
AstroCoords.koe2cart — Method
koe2cart(u::AbstractVector{<:Number}, μ::Number)

Computes the Cartesian Orbital Elements from a Keplerian Set.

Arguments: -'u::AbstractVector{<:Number}': Keplerian State Vector [a; e; i; Ω(RAAN); ω(AOP); f(True Anomaly)] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_cart::Vector{<:Number}': Keplerian Orbital Element Vector [x; y; z; ẋ; ẏ; ż] *All Angles are in Radians

source
AstroCoords.koeM2cart — Method
koeM2cart(u::AbstractVector{<:Number}, μ::Number)

Converts Alternative Keplerian State Vector into the Cartesian State

Arguments: -'u::AbstractVector{<:Number}': Alternative Keplerian State Vector [a; e; i; Ω(RAAN); ω(AOP); M(Mean Anomaly)] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_cart::Vector{<:Number}': Cartesian State Vector [x; y; z; ẋ; ẏ; ż]

source
AstroCoords.meanAnomaly2EccentricAnomaly — Method

Converts the Mean Anomaly into the Eccentric Anomaly

Arguments: -'M::Number': Mean Anomaly of the orbit -'e::Number': Eccentricity of the orbit

Returns -'E::Number': Eccentric Anomaly of the orbit *All angles are in radians

source
AstroCoords.meanAnomaly2TrueAnomaly — Method

Converts the Mean Anomaly into the True Anomaly

Arguments: -'M::Number': Mean Anomaly of the orbit -'e::Number': Eccentricity of the orbit

Returns -'f::Number': Mean Anomaly of the orbit *All angles are in radians

source
AstroCoords.meanMotion — Method

Computes the Keplerian Mean Motion About a Central Body

Arguments:

  • 'X::AstroCoord': Astro Coordinate
  • 'μ::Number': Standard Graviational Parameter of Central Body

Returns:

  • 'n::Number': Orbital Mean Motion
source
AstroCoords.meanMotion — Method

Computes the Keplerian Mean Motion About a Central Body

Arguments:

  • 'a::Number': Semi-Major Axis
  • 'μ::Number': Standard Graviational Parameter of Central Body

Returns:

  • 'n::Number': Orbital Mean Motion
source
AstroCoords.orbitalNRG — Method

Computes the Keplerian Orbital Energy

Arguments: -'X::AstroCoord': Astro Coordinate -'μ::Number': Standard Graviational Parameter of Central Body

Returns -'NRG::Number' - Orbital energy

source
AstroCoords.orbitalNRG — Method

Computes the Keplerian Orbital Energy

Arguments: -'a::Number': AstroCoord State Vector -'μ::Number': Standard Graviational Parameter of Central Body

Returns -'NRG::Number' - Orbital energy

source
AstroCoords.orbitalPeriod — Method

Computes the Keplerian Orbital Period About a Central Body

Arguments:

  • 'X::AstroCoord': Astro Coordinate
  • 'μ::Number': Standard Graviational Parameter of Central Body

Returns:

  • 'T::Number': Orbital Period
source
AstroCoords.orbitalPeriod — Method

Computes the Keplerian Orbital Period About a Central Body

Arguments:

  • 'a::Number': Semi-Major Axis
  • 'μ::Number': Standard Graviational Parameter of Central Body

Returns:

  • 'T::Number': Orbital Period
source
AstroCoords.sphere2cart — Method
sphere2cart(u::AbstractVector{<:Number}, μ::Number)

Computes the Cartesian Orbital Elements from a Spherical Set

Arguments: -'u::AbstractVector{<:Number}': Spherical Orbital Element Vector [r; θ; ϕ; ṙ; θdot; ϕdot] -'μ::Number': Standard Graviational Parameter of Central Body

Returns: -'u_cart::Vector{<:Number}': Cartesian Orbital Element Vector [x; y; z; ẋ; ẏ; ż] *All Angles are in Radians

source
AstroCoords.trueAnomaly2EccentricAnomaly — Method

Converts the True Anomaly into the Mean Anomaly

Arguments: -'f::Number': True Anomaly of the orbit -'e::Number': Eccentricity of the orbit

Returns -'E::Number': Eccentric Anomaly of the orbit *All angles are in radians

source
AstroCoords.trueAnomaly2MeanAnomaly — Method

Converts the True Anomaly into the Mean Anomaly

Arguments: -'f::Number': True Anomaly of the orbit -'e::Number': Eccentricity of the orbit

Returns -'M::Number': Mean Anomaly of the orbit *All angles are in radians

source
Base.inv — Method
inv(trans::Transformation)

Returns the inverse (or reverse) of the transformation trans

source