Documentation

Provides astrodynamical models as AstrodynamicalModels.ODESystems. Check out the ModelingToolkit docs to learn how to use these systems for orbit propagation with DifferentialEquations, or see GeneralAstrodynamics for some convenient orbit propagation wrappers.

Extended help

License

MIT License

Copyright (c) 2023 Joseph D Carpinelli

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Exports

• AttitudeFunction
• AttitudeParameters
• AttitudeState
• AttitudeSystem
• CR3BFunction
• CR3BOrbit
• CR3BParameters
• CR3BState
• CR3BSystem
• CartesianOrbit
• CartesianState
• KeplerianOrbit
• KeplerianParameters
• KeplerianState
• NBFunction
• NBSystem
• Orbit
• OrbitalElements
• PlanarEntryFunction
• PlanarEntryParameters
• PlanarEntryState
• PlanarEntrySystem
• R2BFunction
• R2BOrbit
• R2BParameters
• R2BState
• R2BSystem
• dynamics
• parameters
• state
• system

Imports

• Base
• Core
• DocStringExtensions
• LinearAlgebra
• Memoize
• ModelingToolkit
• SciMLBase
• StaticArrays
• Symbolics

abstract type AstrodynamicalOrbit{U, P}

An abstract supertype for all orbits.

Extended Help

To support the AstrodynamicalOrbit interface, you must implement the following methods.

1. AstrodynamicalModels.states(orbit)
2. AstrodynamicalModels.parameters(orbit)

abstract type AstrodynamicalParameters{F, N} <: StaticArraysCore.FieldVector{N, F}

An abstract supertype for all astrodynamical parameter vectors.

abstract type AstrodynamicalState{F, N} <: StaticArraysCore.FieldVector{N, F}

An abstract supertype for all astrodynamical state vectors.

struct AttitudeParameters{F} <: AstrodynamicalModels.AstrodynamicalParameters{F, 15}

A parameter vector for attitude dynamics.

mutable struct AttitudeState{F} <: AstrodynamicalModels.AstrodynamicalState{F, 7}

A mutable state vector for attitude dynamics.

struct Orbit{var"#s22667"<:CartesianState, var"#s22666"<:CR3BParameters} <: AstrodynamicalModels.AstrodynamicalOrbit{var"#s22667"<:CartesianState, var"#s22666"<:CR3BParameters}

An Orbit which exists within CR3BP dynamics.

struct CR3BParameters{F} <: AstrodynamicalModels.AstrodynamicalParameters{F, 1}

A paremeter vector for CR3BP dynamics.

mutable struct CartesianState{F} <: AstrodynamicalModels.AstrodynamicalState{F, 6}

CartesianState

struct Orbit{var"#s22667"<:CartesianState, P<:(AbstractVector)} <: AstrodynamicalModels.AstrodynamicalOrbit{var"#s22667"<:CartesianState, P<:(AbstractVector)}

An Orbit which exists within R2BP dynamics.

mutable struct CartesianSTM{F} <: StaticArraysCore.FieldMatrix{6, 6, F}

A mutable matrix, with labels, for a 6DOF Cartesian state transition matrix.

mutable struct CartesianState{F} <: AstrodynamicalModels.AstrodynamicalState{F, 6}

A mutable vector, with labels, for 6DOF Cartesian states.

struct Orbit{var"#s22667"<:OrbitalElements, var"#s22666"<:KeplerianParameters} <: AstrodynamicalModels.AstrodynamicalOrbit{var"#s22667"<:OrbitalElements, var"#s22666"<:KeplerianParameters}

An Orbit which exists within Keplerian dynamics.

struct KeplerianParameters{F} <: AstrodynamicalModels.AstrodynamicalParameters{F, 1}

A parameter vector for Keplerian dynamics.

mutable struct OrbitalElements{F} <: AstrodynamicalModels.AstrodynamicalState{F, 6}

OrbitalElements

struct Orbit{U<:(AbstractVector), P<:(AbstractVector)} <: AstrodynamicalModels.AstrodynamicalOrbit{U<:(AbstractVector), P<:(AbstractVector)}

A full representation of an orbit, including a numerical state, and the parameters of the system.

mutable struct OrbitalElements{F} <: AstrodynamicalModels.AstrodynamicalState{F, 6}

A mutable vector, with labels, for 6DOF Keplerian states.

struct PlanarEntryParameters{F} <: AstrodynamicalModels.AstrodynamicalParameters{F, 7}

A parameter vector for planar entry dynamics.

mutable struct PlanarEntryState{F} <: AstrodynamicalModels.AstrodynamicalState{F, 4}

A state vector for planar entry dynamics.

struct Orbit{var"#s22667"<:CartesianState, var"#s22666"<:R2BParameters} <: AstrodynamicalModels.AstrodynamicalOrbit{var"#s22667"<:CartesianState, var"#s22666"<:R2BParameters}

An Orbit which exists within R2BP dynamics.

struct R2BParameters{F} <: AstrodynamicalModels.AstrodynamicalParameters{F, 1}

A parameter vector for R2BP dynamics.

mutable struct CartesianState{F} <: AstrodynamicalModels.AstrodynamicalState{F, 6}

CartesianState

AttitudeFunction(; stm, name, kwargs...)

Returns an ODEFunction for spacecraft attitude dynamics.

Extended Help

Usage

The stm and name keyword arguments are passed to Attitude. All other keyword arguments are passed directly to SciMLBase.ODEFunction.

f = AttitudeFunction()
let u = randn(7), p = randn(15), t = NaN # time invariant
    f(u, p, t)
end

AttitudeSystem(; stm, name, defaults, kwargs...)

A ModelingToolkit.ODESystem for atmospheric entry. Currently, only exponential atmosphere models are provided! The output model is cached with Memoize.jl. Planet-specific parameters default to Earth values.

The order of the states follows: [q₁, q₂, q₃, q₄, ω₁, ω₂, ω₃].

The order of the parameters follows: []

Extended Help

This model describes how an object moves through an exponential atmosphere, above a spherical planet.

States

1. q: scalar-last attitude quaternion
2. ω: body rates (radians per second)

Parameters

1. J: inertial matrix
2. L: lever arm where input torque is applied
3. f: torques on the vehicle body (Newton-meters)

Usage

model = Attitude()

CR3BFunction(; stm, name, kwargs...)

Returns an ODEFunction for CR3B dynamics.

The order of the states follows: [μ].

The order of the parameters follows: [μ].

Extended Help

Usage

The stm, and name keyword arguments are passed to CR3B. All other keyword arguments are passed directly to SciMLBase.ODEFunction.

f = CR3BFunction(; stm=false, jac=true)
let u = randn(6), p = randn(1), t = 0
    f(u, p, t)
end

CR3BProblem(u0, tspan, p; kwargs...)

Return an ODEProblem for the provided CR3B system.

CR3BSystem(; stm, name, defaults, kwargs...)

A ModelingToolkit.ODESystem for the Circular Restricted Three-body Problem.

The order of the states follows: [x, y, z, ẋ, ẏ, ż].

The order of the parameters follows: [μ].

Extended Help

The Circular Restricted Three-body Problem is a simplified dynamical model describing one small body (spacecraft, etc.) and two celestial bodies moving in a circle about their common center of mass. This may seem like an arbitrary simplification, but this assumption holds reasonably well for the Earth-Moon, Sun-Earth, and many other systems in our solar system.

Usage

model = CR3BSystem(; stm=true)

NBFunction(N; stm, name, kwargs...)

Returns an ODEFunction for NBP dynamics. The order of states and parameters in the ODEFunction arguments are equivalent to the order of states and parameters for the system produced with NBP(N). As a general rule, the order of the states follows: [x₁, y₁, z₁, ..., xₙ, yₙ, zₙ, ẋ₁, ẏ₁, ż₁, ..., ẋₙ, ẏₙ, żₙ].

Extended Help

Usage

The stm, and name keyword arguments are passed to NBP. All other keyword arguments are passed directly to SciMLBase.ODEFunction.

f = NBFunction(3; stm=false, name=:NBP, jac=false, sparse=false)
let u = randn(3*6), p = randn(1 + 3), t = 0
    f(u, p, t)
end

NBSystem(N; stm, name, defaults, kwargs...)

A ModelingToolkit.ODESystem for the Newtonian N-body Problem.

The order of the states follows: [x₁, y₁, z₁, ..., xₙ, yₙ, zₙ, ẋ₁, ẏ₁, ż₁, ..., ẋₙ, ẏₙ, żₙ].

The order of the parameters follows: [G, m₁, m₂, ..., mₙ].

Extended Help

The N-body problem is a model which describes how N bodies will move with respect to a common origin. This problem typically involves many bodies which act due to one force: electromagentism, gravity, etc. This model applies most closely to many celestial bodies moving due to gravity. That's about right for a model in a package called AstrodynamicalModels!

Usage

# One model for ALL the planets in our solar system 😎
model = NBSystem(9)

PlanarEntryFunction(; name, kwargs...)

Returns an ODEFunction for Planar Entry dynamics. Results are cached with Memoize.jl.

The order of the states follows: [γ, v, r, θ].

The order of the parameters follows: [R, P, H, m, A, C, μ]

Extended Help

Usage

The name keyword argument is ]passed to PlanarEntry. All other keyword arguments are passed directly to SciMLBase.ODEFunction.

f = PlanarEntryFunction()
let u = randn(4), p = randn(7), t = NaN # time invariant
    f(u, p, t)
end

PlanarEntrySystem(; name, defaults, kwargs...)

A ModelingToolkit.ODESystem for atmospheric entry. Currently, only exponential atmosphere models are provided! The output model is cached with Memoize.jl. Planet-specific parameters default to Earth values.

The order of the states follows: [γ, v, r, θ].

The order of the parameters follows: [R, P, H, m, A, C, μ]

Extended Help

This model describes how an object moves through an exponential atmosphere, above a spherical planet.

Usage

model = PlanarEntrySystem()

R2BFunction(; stm, name, kwargs...)

Returns an ODEFunction for R2B dynamics.

The order of the states follows: [x, y, z, ẋ, ẏ, ż].

The order of the parameters follows: [μ].

Extended Help

Usage

The stm, and name keyword arguments are passed to R2B. All other keyword arguments are passed directly to SciMLBase.ODEFunction.

f = R2BFunction(; stm=false, name=:R2B, jac=true)
let u = randn(6), p = randn(1), t = 0
    f(u, p, t)
end

R2BProblem(u0, tspan, p; kwargs...)

Return an ODEProblem for the provided R2B system.

R2BSystem(; stm, name, defaults, kwargs...)

A ModelingToolkit.ODESystem for the Restricted Two-body Problem.

The order of the states follows: [x, y, z, ẋ, ẏ, ż].

The order of the parameters follows: [μ].

Extended Help

The Restricted Two-body Problem is a simplified dynamical model describing one small body (spacecraft, etc.) and one celestial body. The gravity of the celestial body exhibits a force on the small body. This model is commonly used as a simplification to descibe our solar systems' planets orbiting our sun, or a spacecraft orbiting Earth.

Usage

model = R2BSystem()

dynamics(orbit, args; kwargs...)

Return the underlying dynamics of the system in the form of a ModelingToolkit.ODEFunction.

parameters(orbit)

Return the parameter vector for an Orbit.

state(orbit)

Return the state vector for an Orbit.

system(orbit, args; kwargs...)

Return the underlying dynamics of the system in the form of a ModelingToolkit.ODESystem.