SBPhysicalMatrix33

This class represents a 3x3 physical matrix.

In a physical matrix (e.g., an inertia tensor), all components have the same unit (SBQuantity), so that physical matrices are defined by only one unit.

SBPhysicalMatrix33()                        # a dimensionless 3x3 matrix

There are multiple convenience constructors available for the commonly used physical vectors:

• SBMatrix33
  • SBMatrix33
• SBInverseMass33
  • SBInverseMass33
• SBInverseInertiaTensor33
  • SBInverseInertiaTensor33
• SBMass33
  • SBMass33
• SBInertiaTensor33
  • SBInertiaTensor33

These convenience constructors internally call SBPhysicalMatrix33 with proper SBQuantity and can be used as follows, without specifying the SBQuantity unit:

SBMatrix33(1.0)   # a dimensionless 3x3 matrix with all components equal to 1

Dimensionless 3x3 matrices (SBMatrix33) are especially useful since they are used to represent 3D reference frames, rotation matrices, rigid-body transforms, etc

SBMatrix33(1) == SBPhysicalMatrix33(1)    # True

See also

SAMSON SDK: SBDTypePhysicalMatrix33

class samson.SBPhysicalMatrix33(*args, **kwargs)

Bases: pybind11_object

This class represents 3x3 physical matrices.

SAMSON API: SBDTypePhysicalMatrix33

Overloaded function.

1. __init__(self: samson.SBPhysicalMatrix33) -> None

Constructs a physical matrix with all components set to zero.

2. __init__(self: samson.SBPhysicalMatrix33, d: samson.SBPhysicalVector3) -> None

Constructs the diagonal physical matrix with diagonal [ d.v[0] d.v[1] d.v[2] ].

3. __init__(self: samson.SBPhysicalMatrix33, c0: samson.SBPhysicalVector3, c1: samson.SBPhysicalVector3, c2: samson.SBPhysicalVector3) -> None

Constructs the physical matrix with columns c0, c1, and c2.

4. __init__(self: samson.SBPhysicalMatrix33, mat: list[list[samson.SBQuantity.unitsSI]]) -> None

Constructs the physical matrix from the quantity 2D array mat.

5. __init__(self: samson.SBPhysicalMatrix33, v: samson.SBQuantity.unitsSI) -> None

Constructs the physical matrix with all components set to v.

6. __init__(self: samson.SBPhysicalMatrix33, m00: samson.SBQuantity.unitsSI, m01: samson.SBQuantity.unitsSI, m02: samson.SBQuantity.unitsSI, m10: samson.SBQuantity.unitsSI, m11: samson.SBQuantity.unitsSI, m12: samson.SBQuantity.unitsSI, m20: samson.SBQuantity.unitsSI, m21: samson.SBQuantity.unitsSI, m22: samson.SBQuantity.unitsSI) -> None

Constructs the physical matrix from components m00, m01, m02, m10, m11, m12, m20, m21, and m22.

7. __init__(self: samson.SBPhysicalMatrix33, d: float) -> None

Constructs the dimensionless physical matrix with all components set to d.

8. __init__(self: samson.SBPhysicalMatrix33, mat: list[list[float]]) -> None

Constructs the dimensionless physical matrix from double 2D array mat.

9. __init__(self: samson.SBPhysicalMatrix33, m00: float, m01: float, m02: float, m10: float, m11: float, m12: float, m20: float, m21: float, m22: float) -> None

Constructs the dimensionless physical matrix from components m00, m01, m02, m10, m11, m12, m20, m21, and m22.

__add__(self: samson.SBPhysicalMatrix33, arg0: samson.SBPhysicalMatrix33) → samson.SBPhysicalMatrix33

__eq__(self: samson.SBPhysicalMatrix33, arg0: samson.SBPhysicalMatrix33) → bool

__iadd__(self: samson.SBPhysicalMatrix33, arg0: samson.SBPhysicalMatrix33) → samson.SBPhysicalMatrix33

__imul__(*args, **kwargs)

Overloaded function.

1. __imul__(self: samson.SBPhysicalMatrix33, arg0: float) -> samson.SBPhysicalMatrix33

2. __imul__(self: samson.SBPhysicalMatrix33, arg0: samson.SBQuantity.unitsSI) -> samson.SBPhysicalMatrix33

__isub__(self: samson.SBPhysicalMatrix33, arg0: samson.SBPhysicalMatrix33) → samson.SBPhysicalMatrix33

__itruediv__(*args, **kwargs)

Overloaded function.

1. __itruediv__(self: samson.SBPhysicalMatrix33, arg0: float) -> samson.SBPhysicalMatrix33

2. __itruediv__(self: samson.SBPhysicalMatrix33, arg0: samson.SBQuantity.unitsSI) -> samson.SBPhysicalMatrix33

__mul__(*args, **kwargs)

Overloaded function.

1. __mul__(self: samson.SBPhysicalMatrix33, arg0: float) -> samson.SBPhysicalMatrix33

2. __mul__(self: samson.SBPhysicalMatrix33, arg0: samson.SBPhysicalVector3) -> samson.SBPhysicalVector3

3. __mul__(self: samson.SBPhysicalMatrix33, arg0: samson.SBPhysicalMatrix33) -> samson.SBPhysicalMatrix33

__ne__(self: samson.SBPhysicalMatrix33, arg0: samson.SBPhysicalMatrix33) → bool

__neg__(self: samson.SBPhysicalMatrix33) → samson.SBPhysicalMatrix33

__rmul__(self: samson.SBPhysicalMatrix33, arg0: float) → samson.SBPhysicalMatrix33

__sub__(self: samson.SBPhysicalMatrix33, arg0: samson.SBPhysicalMatrix33) → samson.SBPhysicalMatrix33

__truediv__(self: samson.SBPhysicalMatrix33, arg0: float) → samson.SBPhysicalMatrix33

computeEulerDecompositionZYZ(self: samson.SBPhysicalMatrix33) → list[samson.SBQuantity.unitsSI]

Computes a ZYZ Euler decomposition of this physical matrix.

Returns:

• phi (samson.SBQuantity) – The first Z rotation angle.

• theta (samson.SBQuantity) – The Y rotation angle.

• psi (samson.SBQuantity) – The second Z rotation angle.

cosphi(self: samson.SBPhysicalMatrix33) → samson.SBQuantity.unitsSI

Returns the cosine of the rotation angle of this rotation matrix. This function assumes this physical matrix is a rotation matrix, and returns the cosine of the corresponding rotation angle.

det(self: samson.SBPhysicalMatrix33) → samson.SBQuantity.unitsSI

Returns the determinant of this physical matrix.

diagonalize(self: samson.SBPhysicalMatrix33) → object

Computes the eigenvalues ev and the eigenvectors p of this physical matrix.

Parameters:

• ev (samson.SBVector3) – Stores the eigenvalues when this function returns.

• p (samson.SBMatrix33) – Stores the eigenvectors when this function returns.

static fromAlignment(vectorFrom: samson.SBPhysicalVector3, vectorTo: samson.SBPhysicalVector3) → samson.SBPhysicalMatrix33

Returns the dimensionless physical matrix that transforms vector vectorFrom into vector vectorTo. Precisely, left-multiplying vector vectorFrom by the resulting matrix produces vector vectorTo.

static fromAxisAngle(axis: samson.SBPhysicalVector3, angle: samson.SBQuantity.unitsSI) → samson.SBPhysicalMatrix33

Returns the dimensionless physical matrix corresponding to rotation axis and rotation angle (in radians).

static fromAxisAnglePi(axis: samson.SBPhysicalVector3) → samson.SBPhysicalMatrix33

Returns the dimensionless physical matrix corresponding to rotation axis axis and a rotation angle equal to Pi.

static fromQuaternion(w: samson.SBQuantity.unitsSI, x: samson.SBQuantity.unitsSI, y: samson.SBQuantity.unitsSI, z: samson.SBQuantity.unitsSI) → samson.SBPhysicalMatrix33

Returns the dimensionless physical matrix corresponding to quaternion [ w x y z ]

getColumn(self: samson.SBPhysicalMatrix33, i: int) → samson.SBPhysicalVector3

Returns the i-th column of this physical matrix

getE1(self: samson.SBPhysicalMatrix33) → samson.SBPhysicalVector3

Returns the first column of this physical matrix

getE2(self: samson.SBPhysicalMatrix33) → samson.SBPhysicalVector3

Returns the second column of this physical matrix

getE3(self: samson.SBPhysicalMatrix33) → samson.SBPhysicalVector3

Returns the third column of this physical matrix

getRow(self: samson.SBPhysicalMatrix33, i: int) → samson.SBPhysicalVector3

Returns the i-th row of this physical matrix

static identity() → samson.SBPhysicalMatrix33

Returns an identity physical matrix

inverse(self: samson.SBPhysicalMatrix33) → samson.SBPhysicalMatrix33

Returns the inverse of this physical matrix. This function assumes the physical matrix is invertible and returns its inverse.

makeEulerRotationZYZ(self: samson.SBPhysicalMatrix33, phi: samson.SBQuantity.unitsSI, theta: samson.SBQuantity.unitsSI, psi: samson.SBQuantity.unitsSI) → None

This function sets this physical matrix from ZYZ Euler angles phi, theta and psi.

Parameters:

• phi (samson.SBQuantity) – The first Z rotation angle.

• theta (samson.SBQuantity) – The Y rotation angle.

• psi (samson.SBQuantity) – The second Z rotation angle.

norm(self: samson.SBPhysicalMatrix33) → samson.SBQuantity.unitsSI

Returns the 2-norm of this physical matrix.

orthonormalize(self: samson.SBPhysicalMatrix33) → None

Orthonormalizes this dimensionless physical matrix

quasiStaticUpdate(self: samson.SBPhysicalMatrix33, wx: samson.SBQuantity.unitsSI, wy: samson.SBQuantity.unitsSI, wz: samson.SBQuantity.unitsSI) → object

Performs a quasi-static update of this dimensionless physical matrix using the rotation vector [ wx wy wz ].

Parameters:

• wx (samson.SBQuantity) – The first component of the rotation vector.

• wy (samson.SBQuantity) – The second component of the rotation vector.

• wz (samson.SBQuantity) – The third component of the rotation vector.

Returns:

rotAngle - the rotation angle, rotAxis - the rotation axis, rotA - the rotation axis, rotB - the rotation axis, rotC - the rotation axis.

Return type:

Tuple(samson.SBQuantity, samson.SBVector3, samson.SBMatrix33, samson.SBMatrix33, samson.SBMatrix33)

revoluteJointZAxisMatrix(self: samson.SBPhysicalMatrix33, axis: samson.SBPhysicalVector3) → None

Sets this physical matrix to an orthonormal matrix whose third column is axis

setE1(self: samson.SBPhysicalMatrix33, v: samson.SBPhysicalVector3) → None

Sets the first column of this physical matrix

setE2(self: samson.SBPhysicalMatrix33, v: samson.SBPhysicalVector3) → None

Sets the second column of this physical matrix

setE3(self: samson.SBPhysicalMatrix33, v: samson.SBPhysicalVector3) → None

Sets the third column of this physical matrix

setIdentity(self: samson.SBPhysicalMatrix33) → None

Sets this physical matrix to the identity matrix.

setZero(self: samson.SBPhysicalMatrix33) → None

Sets this physical matrix to zero.

str(self: samson.SBPhysicalMatrix33, fullName: bool = False) → str

Converts the matrix to a string with a full unit name when fullName is True.

swapColumns(self: samson.SBPhysicalMatrix33, i: int, j: int) → None

Swaps columns i and j.

swapRows(self: samson.SBPhysicalMatrix33, i: int, j: int) → None

Swaps rows i and j.

toQuaternion(self: samson.SBPhysicalMatrix33) → list[samson.SBQuantity.unitsSI]

Computes the quaternion [ w x y z ] corresponding to this physical matrix

toRotationVector(self: samson.SBPhysicalMatrix33) → samson.SBPhysicalVector3

Computes the rotation vector corresponding to this dimensionless physical matrix

trace(self: samson.SBPhysicalMatrix33) → samson.SBQuantity.unitsSI

Returns the trace m[0][0] + m[1][1] + m[2][2] of this physical matrix.

transpose(self: samson.SBPhysicalMatrix33) → samson.SBPhysicalMatrix33

Returns the transpose of this physical matrix.

property isDimensionless

Returns True if the matrix is dimensionless

property value