WOLFRAM SYSTEM MODELER
OrientationOrientation object defining rotation from a frame 1 into a frame 2 |
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Wolfram Language
In[1]:=
SystemModel["Modelica.Mechanics.MultiBody.Frames.Orientation"]
Out[1]:=
Information
This information is part of the Modelica Standard Library maintained by the Modelica Association.
This object describes the rotation from a frame 1 into a frame 2. An instance of this type should never be directly accessed but only with the access functions provided in package Modelica.Mechanics.MultiBody.Frames. As a consequence, it is not necessary to know the internal representation of this object as described in the next paragraphs.
"Orientation" is defined to be a record consisting of two elements: "Real T[3,3]", the transformation matrix to rotate frame 1 into frame 2 and "Real w[3]", the angular velocity of frame 2 with respect to frame 1, resolved in frame 2. Element "T" has the following interpretation:
Orientation R;
R.T = [ex, ey, ez];
e.g., R.T = [1,0,0; 0,1,0; 0,0,1]
where ex,ey,ez are unit vectors in the direction of the x-axis, y-axis, and z-axis of frame 1, resolved in frame 2, respectively. Therefore, if v1 is vector v resolved in frame 1 and v2 is vector v resolved in frame 2, the following relationship holds:
v2 = R.T * v1
The inverse orientation R_inv.T = R.TT describes the rotation from frame 2 into frame 1.
Since the orientation is described by 9 variables, there are 6 constraints between these variables. These constraints are defined in function Frames.orientationConstraint.
R.w is the angular velocity of frame 2 with respect to frame 1, resolved
in frame 2. Formally, R.w is defined as:
skew(R.w) = R.T*der(transpose(R.T))
with
| 0 -w[3] w[2] |
skew(w) = | w[3] 0 -w[1] |
| -w[2] w[1] 0 |
Used in Components (29)
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Modelica.Mechanics.MultiBody.Joints Revolute joint (1 rotational degree-of-freedom, 2 potential states, optional axis flange) |
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Modelica.Mechanics.MultiBody.Joints Revolute joint that is described by 2 positional constraints for usage in a planar loop (the ambiguous cut-force perpendicular to the loop and the ambiguous cut-torques are set arbitrarily to zero) |
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Modelica.Mechanics.MultiBody.Joints Spherical joint (3 constraints and no potential states, or 3 degrees-of-freedom and 3 states) |
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Modelica.Mechanics.MultiBody.Joints Free motion joint (6 degrees-of-freedom, 12 potential states) |
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Modelica.Mechanics.MultiBody.Joints Universal - spherical joint aggregation (1 constraint, no potential states) |
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Modelica.Mechanics.MultiBody.Joints.Assemblies Universal - prismatic - spherical joint aggregation (no constraints, no potential states) |
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Modelica.Mechanics.MultiBody.Joints.Constraints Prismatic cut-joint and translational directions may be constrained or released |
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Modelica.Mechanics.MultiBody.Joints.Constraints Revolute cut-joint and translational directions may be constrained or released |
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Modelica.Mechanics.MultiBody.Joints.Constraints Spherical cut joint and translational directions may be constrained or released |
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Modelica.Mechanics.MultiBody.Joints.Constraints Universal cut-joint and translational directions may be constrained or released |
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Modelica.Mechanics.MultiBody.Joints.Internal Revolute joint where the rotation angle is computed from a length constraint (1 degree-of-freedom, no potential state) |
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Modelica.Mechanics.MultiBody.Joints.Internal Internal model to initialize r_rel_a for Joints.FreeMotionScalarInit |
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Modelica.Mechanics.MultiBody.Joints.Internal Internal model to initialize the angels for Joints.FreeMotionScalarInit |
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Modelica.Mechanics.MultiBody.Joints.Internal Internal model to initialize w_rel_b for Joints.FreeMotionScalarInit |
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Modelica.Mechanics.MultiBody.Parts Fixed translation followed by a fixed rotation of frame_b with respect to frame_a |
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Modelica.Mechanics.MultiBody.Parts Rigid body with mass, inertia tensor and one frame connector (12 potential states) |
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Modelica.Mechanics.MultiBody.Parts Rigid body with box shape. Mass and animation properties are computed from box data and density (12 potential states) |
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Modelica.Mechanics.MultiBody.Parts Rigid body with cylinder shape. Mass and animation properties are computed from cylinder data and density (12 potential states) |
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Modelica.Mechanics.MultiBody.Sensors Measure relative angles between two frame connectors |
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Modelica.Mechanics.MultiBody.Sensors.Internal Basic sensor to measure relative angular velocity |
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Modelica.Mechanics.MultiBody.Sensors.Internal Transform absolute vector into another frame |
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Modelica.Mechanics.MultiBody.Sensors.Internal Transform relative vector into another frame |
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Modelica.Mechanics.MultiBody.Visualizers.Advanced Visualizing an arrow with variable size |
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Modelica.Mechanics.MultiBody.Visualizers.Advanced Visualizing a double arrow with variable size |
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Modelica.Mechanics.MultiBody.Visualizers.Advanced Visualizing a pipe with a scalar field |
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Modelica.Mechanics.MultiBody.Visualizers.Internal Visualizing a set of lines as cylinders with variable size, e.g., used to display characters (no Frame connector) |
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Modelica.Utilities.Internal.PartialModelicaServices.Animation Interface for 3D animation of elementary shapes |
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Modelica.Utilities.Internal.PartialModelicaServices.Animation Interface for 3D animation of a vector quantity (force, torque etc) |
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Modelica.Utilities.Internal.PartialModelicaServices.Animation Interface for 3D animation of surfaces |