AttitudeTrajectory¶

AttitudeTrajectory is a chronologically sorted collection of AttitudeState samples (a unit quaternion plus an optional body angular velocity) relating two ReferenceFrame endpoints, with slerp, linear, and Lagrange interpolation.

AttitudeTrajectory has the same API as Trajectory, plus quaternion-aware interpolation and the OrientationProvider accessors (quaternion, angular_velocity, euler_angle, euler_axis, rotation_matrix) documented below.

AttitudeTrajectory ¶

AttitudeTrajectory(frame_a: ReferenceFrame, frame_b: ReferenceFrame)

A chronologically sorted collection of AttitudeState samples relating two ReferenceFrame endpoints.

Every stored quaternion represents the attitude of frame_b relative to frame_a. All states in a trajectory must uniformly carry angular velocity or uniformly omit it; add rejects a state that would mix the two.

Parameters:

Name	Type	Description	Default
`frame_a`	`ReferenceFrame`	Frame endpoint A	required
`frame_b`	`ReferenceFrame`	Frame endpoint B (stored quaternions rotate from frame_a to frame_b)	required

Example

import brahe as bh
from brahe.trajectories import AttitudeTrajectory

traj = bh.AttitudeTrajectory(
    bh.ReferenceFrame.celestial(bh.CelestialFrame.GCRF),
    bh.ReferenceFrame.body(None, bh.BodyFrame.SC_BODY("1")),
)
epoch = bh.Epoch.from_datetime(2024, 1, 1, 0, 0, 0.0, 0.0, bh.TimeSystem.UTC)
traj.add(epoch, bh.Quaternion(1.0, 0.0, 0.0, 0.0))

Initialize instance.

end_epoch `property` ¶

end_epoch: Any

Epoch | None: Last epoch if the trajectory is not empty, None otherwise

frame_a `property` ¶

frame_a: Any

ReferenceFrame: Frame endpoint A

frame_b `property` ¶

frame_b: Any

ReferenceFrame: Frame endpoint B (stored quaternions rotate from frame_a to frame_b)

has_rates `property` ¶

has_rates: Any

bool: True if the trajectory is non-empty and its states carry angular velocity

interpolation_degree `property` ¶

interpolation_degree: Any

int | None: Polynomial degree for Lagrange interpolation, or None unless interpolation_method is "LAGRANGE"

interpolation_method `property` ¶

interpolation_method: Any

str: Current interpolation method - "SLERP", "LINEAR", or "LAGRANGE"

metadata `property` ¶

metadata: dict

dict: Trajectory metadata key-value pairs

name `property` ¶

name: Any

str | None: Trajectory name

start_epoch `property` ¶

start_epoch: Any

Epoch | None: First epoch if the trajectory is not empty, None otherwise

add `method descriptor` ¶

add(epoch: Epoch, quaternion: Quaternion, angular_velocity: ndarray | None = None) -> Any

Add an attitude state at the given epoch.

Parameters:

Name	Type	Description	Default
`epoch`	`Epoch`	Epoch of the new state	required
`quaternion`	`Quaternion`	Unit quaternion attitude, frame A to frame B	required
`angular_velocity`	`ndarray \| None`	Angular velocity of frame B relative to frame A, expressed in frame B. Units: rad/s. Must be uniformly present or uniformly absent across every state added to this trajectory.	`None`

Raises:

Type	Description
`BraheError`	If the new state's angular-velocity presence does not match the trajectory's existing states.

angular_velocity `method descriptor` ¶

angular_velocity(epoch: Epoch) -> Any

Return the body angular velocity at the given epoch.

Returns None when the trajectory carries no rate data (see has_rates); that is not an error.

Parameters:

Name	Type	Description	Default
`epoch`	`Epoch`	Target epoch	required

Returns:

Type	Description
`Any`	numpy.ndarray \| None: Angular velocity of frame B relative to frame A, expressed
`Any`	in frame B, in rad/s, or None if the trajectory carries no rate data

Raises:

Type	Description
`BraheError`	If the epoch lies outside the trajectory's coverage, or the trajectory is empty

euler_angle `method descriptor` ¶

euler_angle(epoch: Epoch, order: EulerAngleOrder) -> EulerAngle

Return the attitude at the given epoch as Euler angles in the requested sequence.

Parameters:

Name	Type	Description	Default
`epoch`	`Epoch`	Target epoch	required
`order`	`EulerAngleOrder`	Euler angle rotation sequence	required

Returns:

Name	Type	Description
`EulerAngle`	`EulerAngle`	Euler angles (radians) at epoch in the requested sequence

Raises:

Type	Description
`BraheError`	If the epoch lies outside the trajectory's coverage, or the trajectory is empty

euler_axis `method descriptor` ¶

euler_axis(epoch: Epoch) -> EulerAxis

Return the attitude at the given epoch as an Euler axis (axis-angle).

Parameters:

Name	Type	Description	Default
`epoch`	`Epoch`	Target epoch	required

Returns:

Name	Type	Description
`EulerAxis`	`EulerAxis`	Unit rotation axis and angle (radians) at epoch

Raises:

Type	Description
`BraheError`	If the epoch lies outside the trajectory's coverage, or the trajectory is empty

quaternion `method descriptor` ¶

quaternion(epoch: Epoch) -> Quaternion

Return the attitude quaternion at the given epoch using the configured interpolation method.

Parameters:

Name	Type	Description	Default
`epoch`	`Epoch`	Target epoch	required

Returns:

Name	Type	Description
`Quaternion`	`Quaternion`	Unit quaternion attitude, frame A to frame B, at epoch

Raises:

Type	Description
`BraheError`	If the epoch lies outside the trajectory's coverage, or the trajectory is empty

rotation_matrix `method descriptor` ¶

rotation_matrix(epoch: Epoch) -> RotationMatrix

Return the attitude at the given epoch as a rotation matrix (DCM).

Parameters:

Name	Type	Description	Default
`epoch`	`Epoch`	Target epoch	required

Returns:

Name	Type	Description
`RotationMatrix`	`RotationMatrix`	3x3 direction cosine matrix at epoch

Raises:

Type	Description
`BraheError`	If the epoch lies outside the trajectory's coverage, or the trajectory is empty

set_interpolation_method `method descriptor` ¶

set_interpolation_method(method: str, degree: int | None = None) -> Any

Set the interpolation method used for state retrieval at arbitrary epochs.

Parameters:

Name	Type	Description	Default
`method`	`str`	Interpolation method - "SLERP" (default), "LINEAR", or "LAGRANGE" (case-insensitive)	required
`degree`	`int \| None`	Polynomial degree, required iff method is "LAGRANGE"	`None`

Raises:

Type	Description
`ValueError`	If method is not recognized, or degree is missing for "LAGRANGE"

AttitudeState ¶

AttitudeState(quaternion: Quaternion, angular_velocity: ndarray | None = None)

A single attitude sample: a unit quaternion and an optional body rate.

The quaternion represents the attitude of frame B relative to frame A (see AttitudeTrajectory). When present, angular_velocity is the angular velocity of frame B relative to frame A, expressed in frame B, in rad/s.

Parameters:

Name	Type	Description	Default
`quaternion`	`Quaternion`	Unit quaternion attitude, frame A to frame B	required
`angular_velocity`	`ndarray \| None`	Angular velocity of frame B relative to frame A, expressed in frame B. Units: rad/s	`None`

Example

import brahe as bh
from brahe.trajectories import AttitudeState
state = AttitudeState(bh.Quaternion(1.0, 0.0, 0.0, 0.0))

Initialize instance.

angular_velocity `property` ¶

angular_velocity: Any

numpy.ndarray | None: Angular velocity of frame B relative to frame A, expressed in frame B, in rad/s, or None if this state does not carry rate data

quaternion `property` ¶

quaternion: Any

Quaternion: Unit quaternion attitude, frame A to frame B

AttitudeTrajectory¶