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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 
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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.

order property 

order: EulerAngleOrder

Get the rotation sequence order.

Returns:

Name Type Description
EulerAngleOrder EulerAngleOrder

Rotation sequence enum value
Example 
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import brahe as bh

e = bh.EulerAngle(bh.EulerAngleOrder.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 
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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 
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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 
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import brahe as bh

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

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 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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import brahe as bh

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