angutils package

Submodules

angutils.angutils module

angutils.angutils.DCM2EulerAng(DCM: ndarray[tuple[int, ...], dtype[float64]], rotSet: List[int] | Tuple[int] | ndarray[tuple[int, ...], dtype[int64]], body: bool = True) → List[float][source]
Parameters:

  • DCM (numpy.ndarray) – Direction Cosine Matrix

  • rotSet (iterable) – 3-element iterable defining order of rotations of a body Euler angle set. See validateEulerAngSet().

  • body (bool) – True for body rotations, False for space rotations. Defaults to True.

Returns:

List of the three computed angles

Return type:

list

angutils.angutils.DCM2axang(DCM: ndarray[tuple[int, ...], dtype[float64]]) → Tuple[ndarray[tuple[int, ...], dtype[float64]], float][source]

Given a direction cosine matrix \({}^\mathcal{B}C^\mathcal{A}\) compute the axis and angle of the rotation. Inverse of calcDCM().

Parameters:

DCM (numpy.ndarray) – 3x3 Direction cosine matrix transforming vector components from frame \(\mathcal{A}\) to frame \(\mathcal{B}\).

Returns:

n (numpy.ndarray):

3x1 matrix representation of the unit vector of the axis of rotation

th (float):

Expression for the angle of rotation. Will always be between 0 and pi

Return type:

tuple

angutils.angutils.EulerAng2DCM(rotSet: List[int] | Tuple[int] | ndarray[tuple[int, ...], dtype[int64]], angs: List[float] | Tuple[float] | ndarray[tuple[int, ...], dtype[float64]], body: bool = True) → ndarray[tuple[int, ...], dtype[float64]][source]

Calculate the equivalent direction cosine matrix for an Euler Angle set

Parameters:

  • rotSet (iterable) – 3-element iterable defining order of rotations of a body Euler angle set. See validateEulerAngSet().

  • angs (iterable) – 3-element iterable of symbols or expressions defining the angle of each rotation.

  • body (bool) – True for body rotations, False for space rotations. Defaults to True.

Returns:

3x3 equivalent direction cosine matrix \({}^\mathcal{B}C^\mathcal{A}\)

Return type:

numpy.ndarray

angutils.angutils.calcDCM(n: List[float] | Tuple[float] | ndarray[tuple[int, ...], dtype[float64]], th: float) → ndarray[tuple[int, ...], dtype[float64]][source]

Rodrigues formula: Calculates the DCM \({}^\mathcal{A}C^\mathcal{B}\) for a rotation of the given angle about a given axis. This is a generalization of rotMat().

Parameters:

  • n (iterable) – 3 element vector representing rotation axis

  • th (float) – Angle of rotation

Returns:

3x3 rotation matrix

Return type:

numpy.ndarray

Note

n need not be normalized - it will automatically be transformed to a unit vector as part of the calculation.

angutils.angutils.calcang(x: _Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], y: _Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], z: _Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) → float[source]

Compute the angle between vectors x and y when rotating counter-clockwise about vector z

Parameters:

  • x (iterable) – 3 components of x vector

  • y (iterable) – 3 components of y vector

  • z (iterable) – 3 components of z vector

Returns:

Angle in radians

Return type:

float

angutils.angutils.colVec(n: _Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) → ndarray[tuple[int, ...], dtype[float64]][source]

Turn any 3-element iterable into a 3x1 column vector

Parameters:

n (iterable) – 3 element iterable

Returns:

3x1 component representation of the vector

Return type:

numpy.ndarray

angutils.angutils.projplane(v: ndarray[tuple[int, ...], dtype[float64]], nv: ndarray[tuple[int, ...], dtype[float64]]) → ndarray[tuple[int, ...], dtype[float64]][source]

Project vectors v onto a plane normal to nv

Parameters:

  • v (numpy.ndarray) – 3xn vectors to be projected

  • nv (numpy.ndarray) – 3x1 or 1x3 components of vector orthogonal to plane of projection

Returns:

Output has equivalent size to v and contains the projected vectors

Return type:

numpy.ndarray

angutils.angutils.rotMat(axis: int, angle: float) → ndarray[tuple[int, ...], dtype[float64]][source]

Returns the DCM \({}^\mathcal{B}C^\mathcal{A}\) for a rotation of the given angle about the specified axis of frame \(\mathcal{A}\)

Parameters:

  • axis (int) – Body axis to rotate about (1, 2, or 3 only)

  • angle (float) – Angle of rotation

Returns:

3x3 rotation matrix

Return type:

numpy.ndarray

angutils.angutils.skew(v: ndarray[tuple[int, ...], dtype[float64]]) → ndarray[tuple[int, ...], dtype[float64]][source]

Given 3x1 vector v, return skew-symmetric matrix

Parameters:

v (iterable) – Component representation of vector. Must have 3 elements

Returns:

3x3 skew-symmetric matrix

Return type:

numpy.ndarray

angutils.angutils.validateEulerAngSet(rotSet: List[int] | Tuple[int] | ndarray[tuple[int, ...], dtype[int64]]) → int[source]

Ensure that a rotation set is valid and return the number of unique elements

Parameters:

rotSet (iterable) – 3-element iterable defining order of rotations of a body Euler angle set. Indexing is 1-based, so valid rotation sets may only contains 1, 2, or 3. A valid rotation set contains exactly 3 elements, at least 2 of which are distinct, and with no rotations about the same axis repeated in a row. [1, 2, 3] and [1, 3, 1] are valid, but [1, 1, 2] is not.

Returns:

Number of unique axes used in rotation (2 or 3).

Return type:

int

angutils.angutils.vnorm(v: ndarray[tuple[int, ...], dtype[float64]]) → ndarray[tuple[int, ...], dtype[float64]][source]

Return components of unit vector of input vector

Parameters:

v (numpy.ndarray) – Components of vector

Returns:

Components of unit vector

Return type:

numpy.ndarray

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