ObjectRotationalMass1D

A 1D rotational inertia (mass) which is attached to Node1D.

Interface

Python names: ObjectRotationalMass1D or Rotor1D, and VRotor1D for its visualization
Nodes it takes: Node1D, NodeGenericODE2, NodePointGround
Body markers that can be placed on it: MarkerBodyPosition, MarkerBodyRigid

Parameters

The parameters of the item; in a dictionary, its type is ‘RotationalMass1D’:

name	type	size	default	description
name	String		‘’	objects’s unique name
inertia	UReal		0.	(symbol: \(J\)) inertia components [SI:kgm\(^2\)] of rotor / rotational mass
nodeNumber	NodeIndex		invalid (-1)	(symbol: \(n0\)) node number (type NodeIndex) of Node1D, providing rotation coordinate \(\psi_0 = c_0\)
referencePosition	Vector3D	3	[0.,0.,0.]	(symbol: \(\LU{0}{\pRef_0}\)) a constant reference position = reference point, used to assign joint constraints accordingly and for drawing
referenceRotation	Matrix3D	9	[[1,0,0], [0,1,0], [0,0,1]]	(symbol: \(\LU{0i}{\Rot_{0}} \in \Rcal^{3 \times 3}\)) an intermediate rotation matrix, which transforms the 1D coordinate into 3D, see description
visualization	VObjectRotationalMass1D			parameters for visualization of item

Renamed parameters, still taken with a DeprecationWarning: physicsInertia (deprecated since 1.12.258, removed in 2031): use inertia.

Visualization parameters

The parameters of VObjectRotationalMass1D, given as visualization:

name	type	size	default	description
show	Bool		True	set true, if item is shown in visualization and false if it is not shown
graphicsData	BodyGraphicsData			Structure contains data for body visualization; data is defined in special list / dictionary structure

Drawing

Drawn as all bodies; its graphicsData, rotated about the axis of its reference rotation by the coordinate of its node.

Output variables

Available as OutputVariableType in sensors, Get...Output() and other functions:

output variable	symbol	description
Position	\(\LU{0}{\pv}\cConfig= \pRefG\)	global position vector; for interpretation see intermediate variables
Displacement	\(\LU{0}{\uv}\cConfig\)	global displacement vector; for interpretation see intermediate variables
Velocity	\(\LU{0}{\vv}\cConfig \)	global velocity vector; for interpretation see intermediate variables
RotationMatrix	\(\LU{0b}{\Rot}\)	vector with 9 components of the rotation matrix (row-major format)
Rotation	\(\theta\)	scalar rotation angle obtained from underlying node
AngularVelocity	\(\LU{0}{\tomega}\cConfig\)	global 3D angular velocity vector of body
AngularVelocityLocal	\(\LU{b}{\tomega}\cConfig\)	local (body-fixed) 3D angular velocity vector of body
KineticEnergy	\(T = \frac{1}{2} J\, \dot \theta_0^2\)	kinetic energy of the rotor; localPosition must be \([0,0,0]\)
PotentialEnergy	\(V = 0\)	the body has no elastic energy; gravity and other loads are not part of it (see exudyn.advancedUtilities.LoadPotentialEnergy) - the value stays the same when a body gets a built-in gravity; localPosition must be \([0,0,0]\)

Detailed description

Definition of quantities

intermediate variables	symbol	description
rotation	\({\theta_0}\cConfig = {c_0}\cConfig + {c_0}\cRef\)	the coordinate \(c_0\) of the node plus its reference value
Position	\(\LU{0}{\pv}\cConfig = \LU{0}{\pRef_0}\)	the constant `referencePosition`
RotationMatrix	\(\LU{0b}{\Rot} = \LU{0i}{\Rot_{0}} \LU{ib}{\mr{\cos(\theta_0)}{-\sin(\theta_0)}{0} {\sin(\theta_0)}{\cos(\theta_0)}{0} {0}{0}{1}}\)	a rotation about the local \(z\)-axis of the frame given by `referenceRotation` \(\LU{0i}{\Rot_{0}}\)
AngularVelocity	\(\LU{0}{\tomega}\cConfig = \LU{0i}{\Rot_{0}} \LU{i}{\vr{0}{0}{\dot \theta_0}}\)	global angular velocity
applied torque	\(\LU{0}{\ttau}_a\)	3D torque from loads, connectors and joints
residual torque	\(\tau\)	the component of the applied torques about the axis

Equations of motion

\[ J \cdot \ddot \theta_0 = \tau , \quad \tau = \LU{i}{[0,\,0,\,1]} \LU{i0}{\Rot_{0}} \LU{0}{\ttau}_a . \]

Marker interfaces

\[ \LU{0}{\Jm_{pos}} = \frac{\partial \LU{0}{\vv}}{\partial \dot \theta_0} = \LU{0b}{\Rot} \left( \LU{b}{\vr{0}{0}{1}} \times \LU{b}{\pv} \right) , \quad \LU{0}{\Jm_{rot}} = \frac{\partial \LU{0}{\tomega}}{\partial \dot \theta_0} = \LU{0i}{\Rot_{0}} \LU{i}{\vr{0}{0}{1}} : \]

a torque acts with its component about the axis, a force at the local position \(\LU{b}{\pv}\) with its moment about the axis - on the axis, \(x = y = 0\), it has no effect; there is no mass-proportional load on it.

Mini example

node = mbs.AddNode(Node1D(referenceCoordinates = [1], #\psi_0ref
                          initialCoordinates=[0.5],   #\psi_0ini
                          initialVelocities=[0.5]))   #\psi_t0ini
rotor = mbs.AddObject(Rotor1D(nodeNumber = node, inertia=1))

#assemble and solve system for default parameters
mbs.Assemble()
mbs.SolveDynamic()

#check result, get current rotor z-rotation at local position [0,0,0]
exu.sys['testResult'] = mbs.GetObjectOutputBody(rotor, exu.OutputVariableType.Rotation, [0,0,0])
#final z-angle of rotor shall be 2

Relevant Examples (Ex) and TestModels (TM) with weblink to github: accessFunctionsTest.py (TM), distanceSensor.py (TM), energiesTest.py (TM), coordinateSpringDamperExt.py (TM), driveTrainTest.py (TM)