christoffel_n.cpp File Reference

Implementation of ChristoffelN. More...

#include "../../include/srfm/tensor/christoffel_n.hpp"
#include <cmath>

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Namespaces
namespace	srfm
namespace	srfm::tensor

Detailed Description

Implementation of ChristoffelN.

See include/srfm/tensor/christoffel_n.hpp for the public API contract.

Algorithm

Christoffel symbols of the second kind:

Γ^λ_μν = ½ g^λσ (∂_μ g_νσ + ∂_ν g_μσ - ∂_σ g_μν)

Metric derivatives are evaluated by central finite differences:

∂_α g_μν ≈ [g_μν(x + h·e_α) - g_μν(x - h·e_α)] / (2h)

For a constant metric (NAssetManifold base case) all derivatives vanish, so all Christoffel symbols are identically zero.

Definition in file christoffel_n.cpp.