Julian Epoch to Besselian Epoch

Transform position and velocity components from Standard Julian Epoch (J2000) to discontinued Standard Besselian Epoch (B1950)

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Libraries:
Aerospace Blockset / Utilities / Axes Transformations

Description

The Julian Epoch to Besselian Epoch block transforms two 3-by-1 vectors of Julian Epoch position $({\bar{r}}_{J 2000})$ , and Julian Epoch velocity $({\bar{v}}_{J 2000})$ into Besselian Epoch position $({\bar{r}}_{B 1950})$ , and Besselian Epoch velocity $({\bar{v}}_{B 1950})$ . For more information on the transformation, see Algorithms.

Ports

Input

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r_J2000 — Position
3-by-1 vector

Position in Standard Julian Epoch (J2000), specified as a 3-by-1 vector.

Data Types: double

v_J2000 — Velocity
3-by-1 vector

Velocity in Standard Julian Epoch (J2000), specified as a 3-by-1 vector.

Data Types: double

Output

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r_B1950 — Position
3-by-1 vector

Position in Standard Besselian Epoch (B1950), returned as a 3-by-1 vector.

Data Types: double

v_B1950 — Velocity
3-by-1 vector

Velocity in Standard Besselian Epoch (B1950), returned as a 3-by-1 vector.

Data Types: double

Algorithms

The transformation is calculated using:

$[\begin{matrix} {\bar{r}}_{B 1950} \\ {\bar{v}}_{B 1950} \end{matrix}] = {[\begin{matrix} {\bar{M}}_{r r} & {\bar{M}}_{v r} \\ {\bar{M}}_{r v} & {\bar{M}}_{v v} \end{matrix}]}^{T} [\begin{matrix} {\bar{r}}_{J 2000} \\ {\bar{v}}_{J 2000} \end{matrix}],$

where

$({\bar{M}}_{r r}, {\bar{M}}_{v r}, {\bar{M}}_{r v}, {\bar{M}}_{v v})$

are defined as:

${\bar{M}}_{r r} = [\begin{matrix} 0.9999256782 & - 0.0111820611 & - 0.0048579477 \\ 0.0111820610 & 0.9999374784 & - 0.0000271765 \\ 0.0048579479 & - 0.0000271474 & 0.9999881997 \end{matrix}]$

${\bar{M}}_{v r} = [\begin{matrix} 0.00000242395018 & - 0.00000002710663 & - 0.00000001177656 \\ 0.00000002710663 & 0.00000242397878 & - 0.00000000006587 \\ 0.00000001177656 & - 0.00000000006582 & 0.00000242410173 \end{matrix}]$

${\bar{M}}_{r v} = [\begin{matrix} - 0.000551 & - 0.238565 & 0.435739 \\ 0.238514 & - 0.002667 & - 0.008541 \\ - 0.435623 & 0.012254 & 0.002117 \end{matrix}]$

${\bar{M}}_{v v} = [\begin{matrix} 0.99994704 & - 0.01118251 & - 0.00485767 \\ 0.01118251 & 0.99995883 & - 0.00002718 \\ 0.00485767 & - 0.00002714 & 1.00000956 \end{matrix}]$

References

[1] "Supplement to Department of Defense World Geodetic System 1984 Technical Report: Part I - Methods, Techniques and Data Used in WGS84 Development," DMA TR8350.2-A.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a

Julian Epoch to Besselian Epoch

Description

Ports

Input

rJ2000 — Position 3-by-1 vector

vJ2000 — Velocity 3-by-1 vector

Output

rB1950 — Position 3-by-1 vector

vB1950 — Velocity 3-by-1 vector

Algorithms

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

r_J2000 — Position
3-by-1 vector

v_J2000 — Velocity
3-by-1 vector

r_B1950 — Position
3-by-1 vector

v_B1950 — Velocity
3-by-1 vector

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.