ROE Transformations¶

Transformations between Keplerian Orbital Elements (KOE/oe) and Relative Orbital Elements (ROE/roe).

Note

For conceptual explanations of the transformation, see ROE Transformations.

state_oe_to_roe `builtin` ¶

state_oe_to_roe(oe_chief: Union[ndarray, Sequence], oe_deputy: Union[ndarray, Sequence], angle_format: AngleFormat, axis: int = -1) -> ndarray

Converts chief and deputy satellite orbital elements (OE) to quasi-nonsingular relative orbital elements (ROE).

The ROE formulation provides a mean description of relative motion that is nonsingular for circular and near-circular orbits. The ROE vector contains: - da: Relative semi-major axis (dimensionless) - dλ: Relative mean longitude (degrees or radians) - dex: x-component of relative eccentricity vector (dimensionless) - dey: y-component of relative eccentricity vector (dimensionless) - dix: x-component of relative inclination vector (degrees or radians) - diy: y-component of relative inclination vector (degrees or radians)

Parameters:

Name	Type	Description	Default
`oe_chief`	`ndarray or list`	Chief satellite orbital elements [a, e, i, Ω, ω, M] shape (6,), or a batch of vectors with the 6 components along `axis` (for example shape (n, 6)).	required
`oe_deputy`	`ndarray or list`	Deputy satellite orbital elements [a, e, i, Ω, ω, M] shape (6,), or a batch of vectors with the 6 components along `axis` (for example shape (n, 6)).	required
`angle_format`	`AngleFormat`	Format of angular elements (DEGREES or RADIANS)	required
`axis`	`int`	The axis along which the 6 components of a single vector lie; the remaining axes enumerate the batch. For a batch of shape (n, 6) the components lie along the last axis, so the default `-1` applies; a (6, n) column layout uses `axis=0`. A single vector in one argument is broadcast across a batch in the other.	`-1`

Returns:

Type	Description
`ndarray`	numpy.ndarray: Relative orbital elements [da, dλ, dex, dey, dix, diy] shape (6,), or the layout of the batched argument for batched input.

Example

import brahe as bh
import numpy as np

# Define chief and deputy orbital elements (degrees)
oe_chief = np.array([bh.R_EARTH + 700e3, 0.001, 97.8, 15.0, 30.0, 45.0])
oe_deputy = np.array([bh.R_EARTH + 701e3, 0.0015, 97.85, 15.05, 30.05, 45.05])

# Convert to ROE
roe = bh.state_oe_to_roe(oe_chief, oe_deputy, bh.AngleFormat.DEGREES)
print(f"Relative orbital elements: {roe}")
# Relative orbital elements: [1.413e-4, 9.321e-2, 4.324e-4, 2.511e-4, 5.0e-2, 4.954e-2]

state_roe_to_oe `builtin` ¶

state_roe_to_oe(oe_chief: Union[ndarray, Sequence], roe: Union[ndarray, Sequence], angle_format: AngleFormat, axis: int = -1) -> ndarray

Converts chief satellite orbital elements (OE) and quasi-nonsingular relative orbital elements (ROE) to deputy satellite orbital elements.

This is the inverse transformation of state_oe_to_roe, converting from ROE representation back to classical orbital elements for the deputy satellite.

Parameters:

Name	Type	Description	Default
`oe_chief`	`ndarray or list`	Chief satellite orbital elements [a, e, i, Ω, ω, M] shape (6,), or a batch of vectors with the 6 components along `axis` (for example shape (n, 6)).	required
`roe`	`ndarray or list`	Relative orbital elements [da, dλ, dex, dey, dix, diy] shape (6,), or a batch of vectors with the 6 components along `axis` (for example shape (n, 6)).	required
`angle_format`	`AngleFormat`	Format of angular elements (DEGREES or RADIANS)	required
`axis`	`int`	The axis along which the 6 components of a single vector lie; the remaining axes enumerate the batch. For a batch of shape (n, 6) the components lie along the last axis, so the default `-1` applies; a (6, n) column layout uses `axis=0`. A single vector in one argument is broadcast across a batch in the other.	`-1`

Returns:

Type	Description
`ndarray`	numpy.ndarray: Deputy satellite orbital elements [a, e, i, Ω, ω, M] shape (6,), or the layout of the batched argument for batched input.

Example

import brahe as bh
import numpy as np

# Define chief orbital elements and ROE (degrees)
oe_chief = np.array([bh.R_EARTH + 700e3, 0.001, 97.8, 15.0, 30.0, 45.0])
roe = np.array([1.413e-4, 9.321e-2, 4.324e-4, 2.511e-4, 5.0e-2, 4.954e-2])

# Convert to deputy OE
oe_deputy = bh.state_roe_to_oe(oe_chief, roe, bh.AngleFormat.DEGREES)
print(f"Deputy orbital elements: {oe_deputy}")
# Deputy orbital elements: [7.079e6, 1.5e-3, 97.85, 15.05, 30.05, 45.05]

ROE Transformations¶

state_oe_to_roe builtin ¶

state_roe_to_oe builtin ¶

state_oe_to_roe `builtin` ¶

state_roe_to_oe `builtin` ¶