Position and 4-velocity state on the manifold. More...

#include <tensor.hpp>

Public Member Functions
GeodesicState	operator+ (const GeodesicState &o) const noexcept
	Pointwise addition of two states (used internally by RK4).

Public Attributes
SpacetimePoint	position
	x^μ: position in financial spacetime

FourVelocity	velocity
	u^μ = dx^μ/dτ: four-velocity tangent vector

Eigen::VectorXd	x
	Position coordinates.

Eigen::VectorXd	u
	Tangent vector (4-velocity, dx/dτ).

Friends
GeodesicState	operator* (double s, const GeodesicState &g) noexcept
	Scalar multiplication (used internally by RK4).

Detailed Description

Position and 4-velocity state on the manifold.

Phase-space state for the geodesic ODE: position x^μ and velocity u^μ.

The geodesic equation is a second-order ODE. We reduce it to first order by treating (x, u) as the state vector: dx^λ/dτ = u^λ du^λ/dτ = −Γ^λ_μν u^μ u^ν

Both vectors must have length equal to the manifold dimension (N+1).

Definition at line 521 of file tensor.hpp.

Member Function Documentation

◆ operator+()

GeodesicState srfm::tensor::GeodesicState::operator+ ( const GeodesicState & o ) const

inlinenoexcept

Pointwise addition of two states (used internally by RK4).

Definition at line 526 of file tensor.hpp.

Friends And Related Symbol Documentation

◆ operator*

GeodesicState operator*	(	double	s,
		const GeodesicState &	g
	)

friend

Scalar multiplication (used internally by RK4).

Definition at line 531 of file tensor.hpp.

Member Data Documentation

◆ position

SpacetimePoint srfm::tensor::GeodesicState::position

x^μ: position in financial spacetime

Definition at line 522 of file tensor.hpp.

◆ u

Eigen::VectorXd srfm::tensor::GeodesicState::u

Tangent vector (4-velocity, dx/dτ).

Definition at line 49 of file geodesic_n.hpp.

◆ velocity

FourVelocity srfm::tensor::GeodesicState::velocity

u^μ = dx^μ/dτ: four-velocity tangent vector

Definition at line 523 of file tensor.hpp.

◆ x

Eigen::VectorXd srfm::tensor::GeodesicState::x

Position coordinates.

Definition at line 48 of file geodesic_n.hpp.

The documentation for this struct was generated from the following files:

include/srfm/tensor.hpp
include/srfm/tensor/geodesic_n.hpp

Public Member Functions

Public Attributes

Friends