ObjectMassPoint

A 3D mass point which is attached to a position-based node, usually NodePoint.

Additional information for ObjectMassPoint:

• This Object has/provides the following types = Body, SingleNoded
• Requested Node type = Position
• Short name for Python = MassPoint
• Short name for Python visualization object = VMassPoint

The item ObjectMassPoint with type = ‘MassPoint’ has the following parameters:

• name [type = String, default = ‘’]:

  objects’s unique name
• physicsMass [$m$, type = UReal, default = 0.]:

  mass [SI:kg] of mass point
• nodeNumber [$n0$, type = NodeIndex, default = invalid (-1)]:

  node number (type NodeIndex) for mass point
• visualization [type = VObjectMassPoint]:

  parameters for visualization of item

The item VObjectMassPoint has the following parameters:

• show [type = Bool, default = True]:

  set true, if item is shown in visualization and false if it is not shown
• graphicsData [type = BodyGraphicsData]:

  Structure contains data for body visualization; data is defined in special list / dictionary structure

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DESCRIPTION of ObjectMassPoint

The following output variables are available as OutputVariableType in sensors, Get…Output() and other functions:

• Position: ${}^0\mathbf{p}{}_{\mathrm{config}}({}^b\mathbf{v})={}^0\mathbf{r}{}_{\mathrm{config}}+{}^0\mathbf{r}{}_{\mathrm{ref}}+{}^{0b}{\mathbf{I}}_{3\times 3}{}^b\mathbf{v}$

  global position vector of translated local position; local (body) coordinate system = global coordinate system
• Displacement: ${}^0\mathbf{u}{}_{\mathrm{config}}=[q_0,q_1,q_2]{}_{\mathrm{config}}{}^{\mathrm{T}}$

  global displacement vector of mass point
• Velocity: ${}^0\mathbf{v}{}_{\mathrm{config}}={}^0\dot{\mathbf{u}}{}_{\mathrm{config}}=[{\dot{q}}_0,{\dot{q}}_1,{\dot{q}}_2]{}_{\mathrm{config}}{}^{\mathrm{T}}$

  global velocity vector of mass point
• Acceleration: ${}^0\mathbf{a}{}_{\mathrm{config}}={}^0\ddot{\mathbf{u}}{}_{\mathrm{config}}=[{\ddot{q}}_0,{\ddot{q}}_1,{\ddot{q}}_2]{}_{\mathrm{config}}{}^{\mathrm{T}}$

  global acceleration vector of mass point

Definition of quantities

intermediate variables	symbol	description
node position	${}^0\mathbf{r}{}_{\mathrm{config}}+{}^0\mathbf{r}{}_{\mathrm{ref}}={}^0\mathbf{p}(n_0){}_{\mathrm{config}}$	position of mass point which is provided by node $n_0$ in any configuration
node displacement	${}^0\mathbf{u}{}_{\mathrm{config}}={}^0\mathbf{r}{}_{\mathrm{config}}=[q_0,q_1,q_2]{}_{\mathrm{config}}{}^{\mathrm{T}}={}^0\mathbf{u}(n_0){}_{\mathrm{config}}$	displacement of mass point which is provided by node $n_0$ in any configuration
node velocity	${}^0\mathbf{v}{}_{\mathrm{config}}=[{\dot{q}}_0,{\dot{q}}_1,{\dot{q}}_2]{}_{\mathrm{config}}{}^{\mathrm{T}}={}^0\mathbf{v}(n_0){}_{\mathrm{config}}$	velocity of mass point which is provided by node $n_0$ in any configuration
transformation matrix	${}^{0b}\mathbf{A}={\mathbf{I}}_{3\times 3}$	transformation of local body ($b$) coordinates to global (0) coordinates; this is the constant unit matrix, because local = global coordinates for the mass point
residual forces	${}^0\mathbf{f}=[f_0,f_1,f_2]{}^{\mathrm{T}}$	residual of all forces on mass point
applied forces	${{}^0\mathbf{f}}_a=[f_0,f_1,f_2]{}^{\mathrm{T}}$	applied forces (loads, connectors, joint reaction forces, …)

Equations of motion

$$\left[\begin{array}{ccc}m& 0& 0\\ 0& m& 0\\ 0& 0& m\end{array}\right]\left[\begin{array}{c}{\ddot{q}}_0\\ {\ddot{q}}_1\\ {\ddot{q}}_2\end{array}\right]=\left[\begin{array}{c}{f}_0\\ f_1\\ f_2\end{array}\right].$$

For example, a LoadCoordinate on coordinate 1 of the node would add a term in $f_1$ on the RHS.

Position-based markers can measure position $\mathbf{p}{}_{\mathrm{config}}$. The position jacobian

$${\mathbf{J}}_{pos}=\partial \mathbf{p}{}_{\mathrm{cur}}/\partial \mathbf{c}{}_{\mathrm{cur}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}\right]$$

transforms the action of global applied forces ${{}^0\mathbf{f}}_a$ of position-based markers on the coordinates $\mathbf{c}$

$$\mathbf{Q}={\mathbf{J}}_{pos}{{}^0\mathbf{f}}_a.$$

MINI EXAMPLE for ObjectMassPoint

node = mbs.AddNode(NodePoint(referenceCoordinates = [1,1,0],
                             initialCoordinates=[0.5,0,0],
                             initialVelocities=[0.5,0,0]))
mbs.AddObject(MassPoint(nodeNumber = node, physicsMass=1))

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

#check result
exudynTestGlobals.testResult = mbs.GetNodeOutput(node, exu.OutputVariableType.Position)[0]
#final x-coordinate of position shall be 2

Relevant Examples and TestModels with weblink:

interactiveTutorial.py (Examples/), ComputeSensitivitiesExample.py (Examples/), coordinateSpringDamper.py (Examples/), massSpringFrictionInteractive.py (Examples/), minimizeExample.py (Examples/), nMassOscillator.py (Examples/), nMassOscillatorInteractive.py (Examples/), parameterVariationExample.py (Examples/), particleClusters.py (Examples/), particlesSilo.py (Examples/), particlesTest.py (Examples/), particlesTest3D.py (Examples/), complexEigenvaluesTest.py (TestModels/), connectorGravityTest.py (TestModels/), contactCoordinateTest.py (TestModels/)

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