EulerAngle Class¶

The EulerAngle class represents attitude using Euler angle sequences for intuitive spacecraft orientation specification.

EulerAngle ¶

EulerAngle(order: str, phi: float, theta: float, psi: float, angle_format: AngleFormat)

Represents a rotation using Euler angles.

Euler angles describe rotations as a sequence of three rotations about specified axes. The rotation sequence is specified by the order parameter (e.g., "XYZ", "ZYX").

Parameters:

Name	Type	Description	Default
`order`	`str`	Rotation sequence (e.g., "XYZ", "ZYX", "ZXZ")	required
`phi`	`float`	First rotation angle in radians or degrees	required
`theta`	`float`	Second rotation angle in radians or degrees	required
`psi`	`float`	Third rotation angle in radians or degrees	required
`angle_format`	`AngleFormat`	Units of input angles (RADIANS or DEGREES)	required

Example

import brahe as bh

# Create Euler angle rotation (roll, pitch, yaw in ZYX order)
e = bh.EulerAngle("ZYX", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
print(f"Roll={e.phi}, Pitch={e.theta}, Yaw={e.psi}")

# Convert to quaternion
q = e.to_quaternion()

# Convert to rotation matrix
dcm = e.to_rotation_matrix()

Initialize instance.

doc `class-attribute` ¶

__doc__ = 'Represents a rotation using Euler angles.\n\nEuler angles describe rotations as a sequence of three rotations about\nspecified axes. The rotation sequence is specified by the order parameter\n(e.g., "XYZ", "ZYX").\n\nArgs:\n    order (str): Rotation sequence (e.g., "XYZ", "ZYX", "ZXZ")\n    phi (float): First rotation angle in radians or degrees\n    theta (float): Second rotation angle in radians or degrees\n    psi (float): Third rotation angle in radians or degrees\n    angle_format (AngleFormat): Units of input angles (RADIANS or DEGREES)\n\nExample:\n    ```python\n    import brahe as bh\n\n    # Create Euler angle rotation (roll, pitch, yaw in ZYX order)\n    e = bh.EulerAngle("ZYX", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)\n    print(f"Roll={e.phi}, Pitch={e.theta}, Yaw={e.psi}")\n\n    # Convert to quaternion\n    q = e.to_quaternion()\n\n    # Convert to rotation matrix\n    dcm = e.to_rotation_matrix()\n    ```'

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to 'utf-8'. errors defaults to 'strict'.

module `class-attribute` ¶

__module__ = 'brahe._brahe'

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to 'utf-8'. errors defaults to 'strict'.

order `property` ¶

order: str

Get the rotation sequence order.

Returns:

Name	Type	Description
`str`	`str`	Rotation sequence (e.g., "XYZ", "ZYX")

Example

import brahe as bh

e = bh.EulerAngle("XYZ", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
print(f"Order: {e.order}")

phi `property` ¶

phi: float

Get the first rotation angle (phi) in radians.

Returns:

Name	Type	Description
`float`	`float`	First rotation angle in radians

Example

import brahe as bh

e = bh.EulerAngle("XYZ", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
print(f"Phi: {e.phi}")

psi `property` ¶

psi: float

Get the third rotation angle (psi) in radians.

Returns:

Name	Type	Description
`float`	`float`	Third rotation angle in radians

Example

import brahe as bh

e = bh.EulerAngle("XYZ", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
print(f"Psi: {e.psi}")

theta `property` ¶

theta: float

Get the second rotation angle (theta) in radians.

Returns:

Name	Type	Description
`float`	`float`	Second rotation angle in radians

Example

import brahe as bh

e = bh.EulerAngle("XYZ", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
print(f"Theta: {e.theta}")

eq `method descriptor` ¶

__eq__(value)

Return self==value.

ge `method descriptor` ¶

__ge__(value)

Return self>=value.

gt `method descriptor` ¶

__gt__(value)

Return self>value.

le `method descriptor` ¶

__le__(value)

Return self<=value.

lt `method descriptor` ¶

__lt__(value)

Return self<value.

ne `method descriptor` ¶

__ne__(value)

Return self!=value.

new `builtin` ¶

__new__(*args, **kwargs)

Create and return a new object. See help(type) for accurate signature.

repr `method descriptor` ¶

__repr__() -> str

Return repr(self).

str `method descriptor` ¶

__str__() -> str

Return str(self).

from_euler_angle `builtin` ¶

from_euler_angle(e: EulerAngle, order: str) -> EulerAngle

Create Euler angles from another Euler angle with different order.

Parameters:

Name	Type	Description	Default
`e`	`EulerAngle`	Source Euler angles	required
`order`	`str`	Desired rotation sequence (e.g., "XYZ", "ZYX")	required

Returns:

Name	Type	Description
`EulerAngle`	`EulerAngle`	Equivalent Euler angles with new order

Example

import brahe as bh

e1 = bh.EulerAngle("XYZ", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
e2 = bh.EulerAngle.from_euler_angle(e1, "ZYX")

from_euler_axis `builtin` ¶

from_euler_axis(e: EulerAxis, order: str) -> EulerAngle

Create Euler angles from an Euler axis representation.

Parameters:

Name	Type	Description	Default
`e`	`EulerAxis`	Euler axis representation	required
`order`	`str`	Desired rotation sequence (e.g., "XYZ", "ZYX")	required

Returns:

Name	Type	Description
`EulerAngle`	`EulerAngle`	Equivalent Euler angles

Example

import brahe as bh
import numpy as np

axis = np.array([0.0, 0.0, 1.0])
ea = bh.EulerAxis(axis, 1.5708, bh.AngleFormat.RADIANS)
e = bh.EulerAngle.from_euler_axis(ea, "XYZ")

from_quaternion `builtin` ¶

from_quaternion(q: Quaternion, order: str) -> EulerAngle

Create Euler angles from a quaternion.

Parameters:

Name	Type	Description	Default
`q`	`Quaternion`	Source quaternion	required
`order`	`str`	Desired rotation sequence (e.g., "XYZ", "ZYX")	required

Returns:

Name	Type	Description
`EulerAngle`	`EulerAngle`	Equivalent Euler angles

Example

import brahe as bh

q = bh.Quaternion(1.0, 0.0, 0.0, 0.0)
e = bh.EulerAngle.from_quaternion(q, "XYZ")

from_rotation_matrix `builtin` ¶

from_rotation_matrix(r: RotationMatrix, order: str) -> EulerAngle

Create Euler angles from a rotation matrix.

Parameters:

Name	Type	Description	Default
`r`	`RotationMatrix`	Rotation matrix	required
`order`	`str`	Desired rotation sequence (e.g., "XYZ", "ZYX")	required

Returns:

Name	Type	Description
`EulerAngle`	`EulerAngle`	Equivalent Euler angles

Example

import brahe as bh
import numpy as np

r = bh.RotationMatrix.from_array(np.eye(3))
e = bh.EulerAngle.from_rotation_matrix(r, "XYZ")

from_vector `builtin` ¶

from_vector(v: ndarray, order: str, angle_format: AngleFormat) -> EulerAngle

Create Euler angles from a numpy array.

Parameters:

Name	Type	Description	Default
`v`	`ndarray`	3-element array [phi, theta, psi]	required
`order`	`str`	Rotation sequence (e.g., "XYZ", "ZYX")	required
`angle_format`	`AngleFormat`	Units of input angles (RADIANS or DEGREES)	required

Returns:

Name	Type	Description
`EulerAngle`	`EulerAngle`	New Euler angle instance

Example

import brahe as bh
import numpy as np

v = np.array([0.1, 0.2, 0.3])
euler = bh.EulerAngle.from_vector(v, "XYZ", bh.AngleFormat.RADIANS)

to_euler_angle `method descriptor` ¶

to_euler_angle(order: str) -> EulerAngle

Convert to Euler angles with different rotation sequence.

Parameters:

Name	Type	Description	Default
`order`	`str`	Desired rotation sequence (e.g., "XYZ", "ZYX")	required

Returns:

Name	Type	Description
`EulerAngle`	`EulerAngle`	Equivalent Euler angles with new order

Example

import brahe as bh

e1 = bh.EulerAngle("XYZ", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
e2 = e1.to_euler_angle("ZYX")

to_euler_axis `method descriptor` ¶

to_euler_axis() -> EulerAxis

Convert to Euler axis representation.

Returns:

Name	Type	Description
`EulerAxis`	`EulerAxis`	Equivalent Euler axis

Example

import brahe as bh

e = bh.EulerAngle("XYZ", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
ea = e.to_euler_axis()

to_quaternion `method descriptor` ¶

to_quaternion() -> Quaternion

Convert to quaternion representation.

Returns:

Name	Type	Description
`Quaternion`	`Quaternion`	Equivalent quaternion

Example

import brahe as bh

e = bh.EulerAngle("XYZ", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
q = e.to_quaternion()

to_rotation_matrix `method descriptor` ¶

to_rotation_matrix() -> RotationMatrix

Convert to rotation matrix representation.

Returns:

Name	Type	Description
`RotationMatrix`	`RotationMatrix`	Equivalent rotation matrix

Example

import brahe as bh

e = bh.EulerAngle("XYZ", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
r = e.to_rotation_matrix()

EulerAngle Class¶

EulerAngle ¶

__doc__ class-attribute ¶

__module__ class-attribute ¶

order property ¶

phi property ¶

psi property ¶

theta property ¶

__eq__ method descriptor ¶

__ge__ method descriptor ¶

__gt__ method descriptor ¶

__le__ method descriptor ¶

__lt__ method descriptor ¶

__ne__ method descriptor ¶

__new__ builtin ¶

__repr__ method descriptor ¶

__str__ method descriptor ¶

from_euler_angle builtin ¶

from_euler_axis builtin ¶

from_quaternion builtin ¶

from_rotation_matrix builtin ¶

from_vector builtin ¶

to_euler_angle method descriptor ¶

to_euler_axis method descriptor ¶

to_quaternion method descriptor ¶

to_rotation_matrix method descriptor ¶

doc `class-attribute` ¶

module `class-attribute` ¶

order `property` ¶

phi `property` ¶

psi `property` ¶

theta `property` ¶

eq `method descriptor` ¶

ge `method descriptor` ¶

gt `method descriptor` ¶

le `method descriptor` ¶

lt `method descriptor` ¶

ne `method descriptor` ¶

new `builtin` ¶

repr `method descriptor` ¶

str `method descriptor` ¶

from_euler_angle `builtin` ¶

from_euler_axis `builtin` ¶

from_quaternion `builtin` ¶

from_rotation_matrix `builtin` ¶

from_vector `builtin` ¶

to_euler_angle `method descriptor` ¶

to_euler_axis `method descriptor` ¶

to_quaternion `method descriptor` ¶

to_rotation_matrix `method descriptor` ¶