MarkerNodeRotationCoordinate

A node-Marker attached to a a node containing rotation; the Marker measures a rotation coordinate (Tait-Bryan angles) or angular velocities on the velocity level.

Interface

Provides: Coordinate
Nodes it can be attached to: NodeRigidBodyEP, NodeRigidBodyRxyz, NodeRigidBodyRotVecLG, NodePointSlope12, NodePointSlope23, NodePointGround
Connectors, constraints and loads that can use it: ObjectConnectorCoordinateSpringDamper, ObjectConnectorCoordinateSpringDamperExt, ObjectConnectorCoordinate, ObjectContactCoordinate, LoadCoordinate

Parameters

The parameters of the item; in a dictionary, its type is ‘NodeRotationCoordinate’:

name	type	default	description
name	String	‘’	marker’s unique name
nodeNumber	NodeIndex	invalid (-1)	node number to which marker is attached to
rotationCoordinate	UInt	invalid (-1)	rotation coordinate: 0=x, 1=y, 2=z; must be given: the default is only a placeholder
visualization	VMarkerNodeRotationCoordinate		parameters for visualization of item

Visualization parameters

VMarkerNodeRotationCoordinate has no parameters.

Drawing

The item draws nothing.

Detailed description

Marker quantities

quantity	symbol	as computed
rotation	\(\varphi_i\)	the Tait-Bryan angle \(i\) = `rotationCoordinate` (0: about \(x\), 1: \(y\), 2: \(z\)), computed from the rotation matrix of the node
its velocity	\(\omega_i\)	component \(i\) of the global angular velocity of the node

The angle is recomputed from the rotation matrix, whatever the rotation parameters of the node are, so it lies in \((-\pi,\,\pi]\) and jumps after a full turn; and \(\omega_i\) is the time derivative of \(\varphi_i\) only while the rotations about the other two axes are small. Use the marker for rotations that stay in that range - a spring about one axis of a nearly planar motion - and a MarkerBodiesRelativeRotationCoordinate or an Euler angle coordinate otherwise.

Jacobians

Row \(i\) of the rotation Jacobian of the node, \(\Jm = \partial \omega_i / \partial \dot\qv\).

Mini example

#a rotation coordinate of a rigid body node, held by a coordinate constraint
inertia = InertiaCuboid(density=1000, sideLengths=[0.4,0.2,0.1])
node = mbs.AddNode(NodeRigidBodyRxyz(referenceCoordinates=[0,0,0, 0,0,0]))
mbs.AddObject(ObjectRigidBody(nodeNumber=node, mass=inertia.Mass(),
                              inertia=inertia.GetInertia6D()))
mRotZ = mbs.AddMarker(MarkerNodeRotationCoordinate(nodeNumber=node, rotationCoordinate=2))
mGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nGround, coordinate=0))
oHold = mbs.AddObject(ObjectConnectorCoordinate(markerNumbers=[mGround, mRotZ]))
mbs.AddLoad(LoadTorqueVector(markerNumber=mbs.AddMarker(MarkerNodeRigid(nodeNumber=node)), loadVector=[0,0,2]))

mbs.Assemble()
mbs.SolveDynamic()

#the constraint holds the rotation about z against the torque: its force is the reaction torque
exu.sys['testResult'] = mbs.GetObjectOutput(oHold, exu.OutputVariableType.Force) #2

Relevant Examples (Ex) and TestModels (TM) with weblink to github: pistonEngine.py (Ex), rigidRotor3DbasicBehaviour.py (Ex), sliderCrank3DwithANCFbeltDrive2.py (Ex), driveTrainTest.py (TM), sliderCrank3Dbenchmark.py (TM)