MarkerBodyPosition

A position body-marker attached to a local (body-fixed) position \(\pLocB = [b_0,\; b_1,\; b_2]\) (\(x\), \(y\), and \(z\) coordinates) of the body. It provides position information as well as the according derivatives (=velocity and derivative of position w.r.t. body coordinates). It can be used for connectors, joints or loads where position is required. If connectors also require orientation information, use a MarkerBodyRigid.

Additional information for MarkerBodyPosition:

• This Marker has/provides the following types = Object, Body, Position

The item MarkerBodyPosition with type = ‘BodyPosition’ has the following parameters:

• name [type = String, default = ‘’]:

  marker’s unique name
• bodyNumber [type = ObjectIndex, default = invalid (-1)]:

  body number to which marker is attached to
• localPosition [\(\pLocB\), type = Vector3D, size = 3, default = [0.,0.,0.]]:

  local body position of marker; e.g. local (body-fixed) position where force is applied to
• visualization [type = VMarkerBodyPosition]:

  parameters for visualization of item

The item VMarkerBodyPosition has the following parameters:

• show [type = Bool, default = True]:

  set true, if item is shown in visualization and false if it is not shown

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DESCRIPTION of MarkerBodyPosition

The body position marker provides an interface to a object of type body (ObjectGround, ObjectMassPoint, ObjectRigidBody, …) and provides access to kinematic quantities such as position and velocityand to the position jacobian, using a localPosition \(\pLocB\) which is defined within the local coordinates of the body (\(b\)). The kinematic quantities are computed according to the definition of output variables in the respective bodies.

The position jacobian represents the derivative of the node position \({\mathbf{p}}_\mathrm{n}\) with all nodal coordinates,

\[\LU{0}{{\mathbf{J}}_\mathrm{pos}} = \frac{\partial \LU{0}{{\mathbf{p}}_\mathrm{n}}}{\partial {\mathbf{q}}_\mathrm{n}}\]

and it is usually computed as the derivative of the (global) translational velocity w.r.t.velocity coordinates,

\[\LU{0}{{\mathbf{J}}_\mathrm{pos}} = \frac{\partial \LU{0}{{\mathbf{v}}_\mathrm{n}}}{\partial \dot {\mathbf{q}}_\mathrm{n}}\]

As an example of the ObjectRigidBody2D, see Section ObjectRigidBody2D, the position and velocity are computed as

\[\LU{0}{{\mathbf{p}}}\cConfig(\pLocB) = \LU{0}{\pRef}\cConfig + \LU{0}{\pRef}\cRef + \LU{0b}{\Rot}\pLocB ,\]

\[\LU{0}{{\mathbf{v}}}\cConfig(\pLocB) = \LU{0}{\dot{\mathbf{u}}}\cConfig + \LU{0b}{\Rot}(\LU{b}{\tomega} \times \pLocB\cConfig) .\]

Thus, the position jacobian for ObjectRigidBody2D reads

\[\LU{0}{{\mathbf{J}}_\mathrm{pos}^{\mathrm{NodeRigidBody2D}}} = \mr{1}{0}{-\sin\theta_0 \LU{b}{b_0} - \cos\theta_0 \LU{b}{b_1}} {0}{1}{\cos\theta_0 \LU{b}{b_0} - \sin\theta_0 \LU{b}{b_1}} {0}{0}{0}\]

For details, see the respective definition of the body and the C++ implementation.

Relevant Examples and TestModels with weblink:

ANCFcontactCircle.py (Examples/), ANCFcontactCircle2.py (Examples/), ANCFmovingRigidbody.py (Examples/), ANCFslidingJoint2D.py (Examples/), ANCFslidingJoint2Drigid.py (Examples/), ANCFswitchingSlidingJoint2D.py (Examples/), beltDrivesComparison.py (Examples/), bungeeJump.py (Examples/), coordinateSpringDamper.py (Examples/), finiteSegmentMethod.py (Examples/), flexibleRotor3Dtest.py (Examples/), geneticOptimizationSliderCrank.py (Examples/), ANCFcontactCircleTest.py (TestModels/), ANCFcontactFrictionTest.py (TestModels/), ANCFmovingRigidBodyTest.py (TestModels/)

The web version may not be complete. For details, consider also the Exudyn PDF documentation : theDoc.pdf