Models

All names on this page are provided by version 3.8.0 of AstrodynamicalModels. For more information, consult the documentation for AstrodynamicalModels directly.

AstrodynamicalModels

Provides astrodynamical models as AstrodynamicalModels.System instances. 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
• CartesianSTM
• CartesianState
• KeplerianOrbit
• KeplerianParameters
• KeplerianState
• NBFunction
• NBSystem
• Orbit
• OrbitalElements
• PlanarEntryFunction
• PlanarEntryParameters
• PlanarEntryState
• PlanarEntrySystem
• R2BFunction
• R2BOrbit
• R2BParameters
• R2BState
• R2BSystem
• dynamics
• parameters
• state
• system

Imports

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

AttitudeFunction

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

AttitudeParameters

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

A parameter vector for attitude dynamics.

AttitudeState

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

A mutable state vector for attitude dynamics.

AttitudeSystem

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

A ModelingToolkit.System 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

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

CR3BOrbit

struct Orbit{var"#s83"<:CartesianState, var"#s82"<:CR3BParameters} <: AstrodynamicalModels.AstrodynamicalOrbit{var"#s83"<:CartesianState, var"#s82"<:CR3BParameters}

An Orbit which exists within CR3BP dynamics.

Return a CR3BP orbit with parameters associated with the provided body in nondimensional units.

CR3BParameters

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

A parameter vector for CR3BP dynamics.

Return the CR3BP parameters associated with the provided body in nondimensional units.

CR3BState

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

CartesianState

CR3BSystem

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

A ModelingToolkit.System 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)

CartesianOrbit

struct Orbit{var"#s83"<:CartesianState, P<:(AbstractVector)} <: AstrodynamicalModels.AstrodynamicalOrbit{var"#s83"<:CartesianState, P<:(AbstractVector)}

An Orbit which exists within R2BP dynamics.

CartesianSTM

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

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

CartesianState

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

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

KeplerianOrbit

struct Orbit{var"#s83"<:OrbitalElements, var"#s82"<:KeplerianParameters} <: AstrodynamicalModels.AstrodynamicalOrbit{var"#s83"<:OrbitalElements, var"#s82"<:KeplerianParameters}

An Orbit which exists within Keplerian dynamics.

Return a Keplerian orbit with parameters associated with the provided body (KM^3/S2).

KeplerianParameters

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

A parameter vector for Keplerian dynamics.

Return the Keplerian parameters associated with the provided body (KM^3/S2).

KeplerianState

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

OrbitalElements

NBFunction

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].

NoteNote

Unlike R2BP and CR3BP, jac is set to false by default. The number of states for NBP systems can be very large for relatively small numbers of bodies (N). Enabling jac=true by default would cause unnecessarily long waiting times for this (memoize?) function to return for N ≥ 3 or so. If N=2 and stm=true, setting jac=true could still result in several minutes of calculations, depending on the computer you’re using.

WarningWarning

Be careful about specifying stm=true for systems with N ≥ 3! If state transition matrix dynamics are enabled, you can calculate the total number of system states with N*6 + (N*6)^2. Note that this increases exponentially as N grows! For N == 6, unless you’re using parallelization, your computer may run for several hours.

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

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

A ModelingToolkit.System 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].

WarningWarning

Be careful about specifying stm=true for systems with N ≥ 3! If state transition matrix dynamics are enabled, you can calculate the total number of system states with N*6 + (N*6)^2. Note that this increases exponentially as N grows! For N == 6, unless you’re using parallelization, your computer may run for several hours.

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)

Orbit

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.

Return an orbit with parameters associated with the provided body (KM^3/S2).

OrbitalElements

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

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

PlanarEntryFunction

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

PlanarEntryParameters

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

A parameter vector for planar entry dynamics.

PlanarEntryState

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

A state vector for planar entry dynamics.

PlanarEntrySystem

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

A ModelingToolkit.System 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

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

R2BOrbit

struct Orbit{var"#s83"<:CartesianState, var"#s82"<:R2BParameters} <: AstrodynamicalModels.AstrodynamicalOrbit{var"#s83"<:CartesianState, var"#s82"<:R2BParameters}

An Orbit which exists within R2BP dynamics.

Return a R2BP orbit with parameters associated with the provided body (KM^3/S2).

R2BParameters

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

A parameter vector for R2BP dynamics.

Return the R2BP parameters associated with the provided body (KM^3/S2).

R2BState

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

CartesianState

R2BSystem

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

A ModelingToolkit.System 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 describe our solar systems’ planets orbiting our sun, or a spacecraft orbiting Earth.

Usage

model = R2BSystem()

dynamics

dynamics(orbit, args; kwargs...)

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

parameters

parameters(orbit)

Return the parameter vector for an Orbit.

state

state(orbit)

Return the state vector for an Orbit.

system

system(orbit, args; kwargs...)

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