Utility Functions

CRTBPNaturalMotion.jacobi_integral — Method

jacobi_integral(x, μ)

Computes the Jacobi integral for the CRTBP given the state x and mass parameter μ.

Arguments

x::AbstractVector: State vector.
μ::Real: Mass parameter.

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CRTBPNaturalMotion.derivative — Method

derivative(m::FastChebInterpolation{1}, τ1) where IT -> SVector{6, Float64}

Evaluate the derivative of the interpolation at the given τ1 for a uni-variate interpolation.

Arguments

m::FastChebInterpolation{IT}: The interpolation object.
τ1: The variable.

Returns

SVector{6, Float64}: The derivative of the interpolation.

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CRTBPNaturalMotion.hessian — Method

hessian(m::FastChebInterpolation{1}, τ1, τ2) -> SMatrix{6, 1, Float64, 6}

Evaluate the Hessian of the interpolation at the given τ1. This computes the second derivative of the interpolation at the given τ1 for a uni-variate interpolation and returns a SMatrix{6, 1, Float64, 6} (rather than an SVector{6, Float64} like second_derivative).

Arguments

m::FastChebInterpolation{IT}: The interpolation object.
τ1: The variable.

Returns

SMatrix{6, 1, Float64, 6}: The Hessian of the interpolation.

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CRTBPNaturalMotion.hessian — Method

hessian(m::FastChebInterpolation{2}, τ1, τ2) -> SArray{Tuple{6, 2, 2}, Float64, 3, 24}

Evaluate the Hessian of the interpolation at the given τ1 and τ2. This computes the second derivative of the interpolation at the given τ1 and τ2 for a bi-variate interpolation and returns a SArray{Tuple{6, 2, 2}, Float64, 3, 24}.

Arguments

m::FastChebInterpolation{IT}: The interpolation object.
τ1: The first variable.
τ2: The second variable.

Returns

SArray{Tuple{6, 2, 2}, Float64, 3, 24}: The Hessian of the interpolation.

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CRTBPNaturalMotion.jacobian — Method

jacobian(m::FastChebInterpolation{1}, τ1) where IT -> SMatrix{6, 1, Float64, 6}

Evaluate the Jacobian of the interpolation at the given τ1 for a uni-variate interpolation.

Arguments

m::FastChebInterpolation{IT}: The interpolation object.
τ1: The variable.

Returns

SMatrix{6, 1, Float64, 6}: The Jacobian of the interpolation.

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CRTBPNaturalMotion.jacobian — Method

jacobian(m::FastChebInterpolation{2}, τ1, τ2) where IT -> SMatrix{6, 2, Float64, 12}

Evaluate the Jacobian of the interpolation at the given τ1 and τ2 for a bi-variate interpolation.

Arguments

m::FastChebInterpolation{IT}: The interpolation object.
τ1: The first variable.
τ2: The second variable.

Returns

SMatrix{6, 2, Float64, 12}: The Jacobian of the interpolation.

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CRTBPNaturalMotion.load_interp — Method

load_interp(file::String) -> FastChebInterpolation{IT}

Load an interpolation object from a file.

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CRTBPNaturalMotion.save_interp — Method

save_interp(file::String, it::FastChebInterpolation{IT}) where IT

Save the interpolation object to a file.

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CRTBPNaturalMotion.second_derivative — Method

second_derivative(m::FastChebInterpolation{1}, τ1) -> SVector{6, Float64}

Evaluate the second derivative of the interpolation at the given τ1 for a uni-variate interpolation. The second derivatives are computed by employing Enzyme to differentiate the analytical computation of the first derivative.

Arguments

m::FastChebInterpolation{IT}: The interpolation object.
τ1: The variable.

Returns

SVector{6, Float64}: The second derivative of the interpolation.

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CRTBPNaturalMotion.value — Method

value(m::FastChebInterpolation{N}, τ1[, τ2]) -> SVector{6, Float64}

Evaluate the interpolation at the given τ1 and τ2 (if employing a bi-variate interpolation).

Arguments

m::FastChebInterpolation{IT}: The interpolation object.
τ1: The variable.
τ2: The second variable (if employing a bi-variate interpolation).

Returns

SVector{6, Float64}: The interpolated state.

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