EulerAxis Class¶

The EulerAxis class represents attitude using axis-angle representation (Euler's rotation theorem).

EulerAxis ¶

EulerAxis(axis: ndarray, angle: float, angle_format: AngleFormat)

Represents a rotation using Euler axis-angle representation.

The Euler axis-angle representation describes a rotation as a single rotation about a specified axis by a given angle. This is also known as the axis-angle or rotation vector representation.

Parameters:

Name	Type	Description	Default
`axis`	`ndarray`	3-element unit vector specifying rotation axis	required
`angle`	`float`	Rotation angle in radians or degrees	required
`angle_format`	`AngleFormat`	Units of input angle (RADIANS or DEGREES)	required

Example

import brahe as bh
import numpy as np

# Rotation of 90 degrees about z-axis
axis = np.array([0.0, 0.0, 1.0])
e = bh.EulerAxis(axis, np.pi/2, bh.AngleFormat.RADIANS)
print(f"Angle: {e.angle} rad")

# Convert to quaternion
q = e.to_quaternion()

Initialize instance.

doc `class-attribute` ¶

__doc__ = 'Represents a rotation using Euler axis-angle representation.\n\nThe Euler axis-angle representation describes a rotation as a single rotation\nabout a specified axis by a given angle. This is also known as the axis-angle\nor rotation vector representation.\n\nArgs:\n    axis (numpy.ndarray): 3-element unit vector specifying rotation axis\n    angle (float): Rotation angle in radians or degrees\n    angle_format (AngleFormat): Units of input angle (RADIANS or DEGREES)\n\nExample:\n    ```python\n    import brahe as bh\n    import numpy as np\n\n    # Rotation of 90 degrees about z-axis\n    axis = np.array([0.0, 0.0, 1.0])\n    e = bh.EulerAxis(axis, np.pi/2, bh.AngleFormat.RADIANS)\n    print(f"Angle: {e.angle} rad")\n\n    # Convert to quaternion\n    q = e.to_quaternion()\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'.

angle `property` ¶

angle: float

Get the rotation angle in radians.

Returns:

Name	Type	Description
`float`	`float`	Rotation angle in radians

Example

import brahe as bh
import numpy as np

axis = np.array([0.0, 0.0, 1.0])
e = bh.EulerAxis(axis, 1.5708, bh.AngleFormat.RADIANS)
print(f"Angle: {e.angle}")

axis `property` ¶

axis: ndarray

Get the rotation axis as a numpy array.

Returns:

Type	Description
`ndarray`	numpy.ndarray: 3-element unit vector specifying rotation axis

Example

import brahe as bh
import numpy as np

axis = np.array([0.0, 0.0, 1.0])
e = bh.EulerAxis(axis, 1.5708, bh.AngleFormat.RADIANS)
print(f"Axis: {e.axis}")

eq `method descriptor` ¶

__eq__(value)

Return self==value.

ge `method descriptor` ¶

__ge__(value)

Return self>=value.

getitem `method descriptor` ¶

__getitem__(key: str) -> Any

Return self[key].

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) -> EulerAxis

Create an Euler axis from Euler angles.

Parameters:

Name	Type	Description	Default
`e`	`EulerAngle`	Euler angle representation	required

Returns:

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

Example

import brahe as bh

euler = bh.EulerAngle("XYZ", 0.1, 0.2, 0.3, bh.AngleFormat.RADIANS)
e = bh.EulerAxis.from_euler_angle(euler)

from_euler_axis `builtin` ¶

from_euler_axis(e: EulerAxis) -> EulerAxis

Create an Euler axis from another Euler axis (copy constructor).

Parameters:

Name	Type	Description	Default
`e`	`EulerAxis`	Source Euler axis	required

Returns:

Name	Type	Description
`EulerAxis`	`EulerAxis`	New Euler axis instance

Example

import brahe as bh
import numpy as np

axis = np.array([0.0, 0.0, 1.0])
e1 = bh.EulerAxis(axis, 1.5708, bh.AngleFormat.RADIANS)
e2 = bh.EulerAxis.from_euler_axis(e1)

from_quaternion `builtin` ¶

from_quaternion(q: Quaternion) -> EulerAxis

Create an Euler axis from a quaternion.

Parameters:

Name	Type	Description	Default
`q`	`Quaternion`	Source quaternion	required

Returns:

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

Example

import brahe as bh

q = bh.Quaternion(1.0, 0.0, 0.0, 0.0)
e = bh.EulerAxis.from_quaternion(q)

from_rotation_matrix `builtin` ¶

from_rotation_matrix(r: RotationMatrix) -> EulerAxis

Create an Euler axis from a rotation matrix.

Parameters:

Name	Type	Description	Default
`r`	`RotationMatrix`	Rotation matrix	required

Returns:

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

Example

import brahe as bh
import numpy as np

r = bh.RotationMatrix.from_array(np.eye(3))
e = bh.EulerAxis.from_rotation_matrix(r)

from_values `builtin` ¶

from_values(x: float, y: float, z: float, angle: float, angle_format: AngleFormat) -> EulerAxis

Create an Euler axis from individual axis components and angle.

Parameters:

Name	Type	Description	Default
`x`	`float`	X component of rotation axis	required
`y`	`float`	Y component of rotation axis	required
`z`	`float`	Z component of rotation axis	required
`angle`	`float`	Rotation angle in radians or degrees	required
`angle_format`	`AngleFormat`	Units of input angle (RADIANS or DEGREES)	required

Returns:

Name	Type	Description
`EulerAxis`	`EulerAxis`	New Euler axis instance

Example

import brahe as bh

e = bh.EulerAxis.from_values(0.0, 0.0, 1.0, 1.5708, bh.AngleFormat.RADIANS)

from_vector `builtin` ¶

from_vector(v: ndarray, angle_format: AngleFormat, vector_first: bool) -> EulerAxis

Create an Euler axis from a numpy array.

Parameters:

Name	Type	Description	Default
`v`	`ndarray`	4-element array containing axis and angle	required
`angle_format`	`AngleFormat`	Units of angle (RADIANS or DEGREES)	required
`vector_first`	`bool`	If True, array is [x, y, z, angle], else [angle, x, y, z]	required

Returns:

Name	Type	Description
`EulerAxis`	`EulerAxis`	New Euler axis instance

Example

import brahe as bh
import numpy as np

v = np.array([0.0, 0.0, 1.0, 1.5708])
e = bh.EulerAxis.from_vector(v, bh.AngleFormat.RADIANS, True)

to_euler_angle `method descriptor` ¶

to_euler_angle(order: str) -> EulerAngle

Convert to Euler angle representation.

Parameters:

Name	Type	Description	Default
`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 = ea.to_euler_angle("XYZ")

to_euler_axis `method descriptor` ¶

to_euler_axis() -> EulerAxis

Convert to Euler axis representation (returns self).

Returns:

Name	Type	Description
`EulerAxis`	`EulerAxis`	This Euler axis

Example

import brahe as bh
import numpy as np

axis = np.array([0.0, 0.0, 1.0])
e1 = bh.EulerAxis(axis, 1.5708, bh.AngleFormat.RADIANS)
e2 = e1.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
import numpy as np

axis = np.array([0.0, 0.0, 1.0])
e = bh.EulerAxis(axis, 1.5708, 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
import numpy as np

axis = np.array([0.0, 0.0, 1.0])
e = bh.EulerAxis(axis, 1.5708, bh.AngleFormat.RADIANS)
r = e.to_rotation_matrix()

to_vector `method descriptor` ¶

to_vector(angle_format: AngleFormat, vector_first: bool) -> ndarray

Convert Euler axis to a numpy array.

Parameters:

Name	Type	Description	Default
`angle_format`	`AngleFormat`	Units for output angle (RADIANS or DEGREES)	required
`vector_first`	`bool`	If True, returns [x, y, z, angle], else [angle, x, y, z]	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: 4-element array containing axis and angle

EulerAxis Class¶

EulerAxis ¶

__doc__ class-attribute ¶

__module__ class-attribute ¶

angle property ¶

axis property ¶

__eq__ method descriptor ¶

__ge__ method descriptor ¶

__getitem__ 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_values builtin ¶

from_vector builtin ¶

to_euler_angle method descriptor ¶

to_euler_axis method descriptor ¶

to_quaternion method descriptor ¶

to_rotation_matrix method descriptor ¶

to_vector method descriptor ¶

doc `class-attribute` ¶

module `class-attribute` ¶

angle `property` ¶

axis `property` ¶

eq `method descriptor` ¶

ge `method descriptor` ¶

getitem `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_values `builtin` ¶

from_vector `builtin` ¶

to_euler_angle `method descriptor` ¶

to_euler_axis `method descriptor` ¶

to_quaternion `method descriptor` ¶

to_rotation_matrix `method descriptor` ¶

to_vector `method descriptor` ¶