ObjectMassPoint

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

Simpler: mbs.CreateMassPoint adds this item, with what it needs, in one call.

Interface

Python names: ObjectMassPoint or MassPoint, and VMassPoint for its visualization
Nodes it takes: NodePoint, NodeRigidBodyEP, NodeRigidBodyRxyz, NodeRigidBodyRotVecLG, NodePointSlope1, NodePointSlope12, NodePointSlope23, NodePointGround
Body markers that can be placed on it: MarkerBodyMass, MarkerBodyPosition

Parameters

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

name	type	default	description
name	String	‘’	objects’s unique name
mass	UReal	0.	(symbol: \(m\)) mass [SI:kg] of mass point
nodeNumber	NodeIndex	invalid (-1)	(symbol: \(n0\)) node number (type NodeIndex) for mass point
visualization	VObjectMassPoint		parameters for visualization of item

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

Visualization parameters

The parameters of VObjectMassPoint, 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, moved with the node; without graphicsData only the node is seen.

Output variables

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

output variable	symbol	description
Position	\(\LU{0}{\pv}\cConfig(\pLocB) = \LU{0}{\pRef}\cConfig + \LU{0}{\pRef}\cRef + \LU{0b}{\ImThree}\pLocB\)	global position vector of translated local position; local (body) coordinate system = global coordinate system
Displacement	\(\LU{0}{\uv}\cConfig = [q_0,\;q_1,\;q_2]\cConfig\tp\)	global displacement vector of mass point
Velocity	\(\LU{0}{\vv}\cConfig = \LU{0}{\dot\uv}\cConfig = [\dot q_0,\;\dot q_1,\;\dot q_2]\cConfig\tp\)	global velocity vector of mass point
Acceleration	\(\LU{0}{\av}\cConfig = \LU{0}{\ddot\uv}\cConfig = [\ddot q_0,\;\ddot q_1,\;\ddot q_2]\cConfig\tp\)	global acceleration vector of mass point
RotationMatrix		identity matrix (only for completeness)
Rotation	\([0,0,0]\)	(only for completeness)
AngularVelocity	\([0,0,0]\)	(only for completeness)
AngularVelocityLocal	\([0,0,0]\)	(only for completeness)
KineticEnergy	\(T = \frac{1}{2} m\, \LU{0}{\vv}\tp \LU{0}{\vv}\)	kinetic energy of the mass point; 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
node position	\(\LU{0}{\pv}\cConfig = \LU{0}{\pRef}\cRef + \LU{0}{\uv}\cConfig = \LU{0}{\pv}(n_0)\cConfig\)	position of the mass point, provided by node \(n_0\), in any configuration
node displacement	\(\LU{0}{\uv}\cConfig = [q_0,\;q_1,\;q_2]\cConfig\tp\)	displacement of the mass point, the coordinates of node \(n_0\)
node velocity	\(\LU{0}{\vv}\cConfig = [\dot q_0,\;\dot q_1,\;\dot q_2]\cConfig\tp\)	velocity of the mass point
rotation matrix	\(\LU{0b}{\Rot} = \ImThree\)	the body frame is the global frame
applied forces	\(\LU{0}{\fv}_a = [f_0,\;f_1,\;f_2]\tp\)	from loads, connectors and joint reaction forces

Equations of motion

\[ \mr{m}{0}{0} {0}{m}{0} {0}{0}{m} \vr{\ddot q_0}{\ddot q_1}{\ddot q_2} = \vr{f_0}{f_1}{f_2} . \]

A LoadCoordinate on coordinate 1 of the node adds to \(f_1\).

Marker interfaces

The position of a local point is \(\LU{0}{\pv}\cConfig + \pLocB\), as the body frame is the global frame. The position Jacobian is the unit matrix,

\[ \LU{0}{\Jm_{pos}} = \frac{\partial \LU{0}{\vv}}{\partial \dot\qv} = \mr{1}{0}{0} {0}{1}{0} {0}{0}{1} , \]

so a global force acts as it is, \(\Qm = \LU{0}{\fv}_a\), and the mass-weighted Jacobian is \(m\) times it. A mass point has no rotation: there is no rotation Jacobian, and no MarkerBodyRigid fits.

Mini example

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

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

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

Examples (Ex) and TestModels (TM) that show this item, with weblink to github: basicTutorial2024.py (Ex), tutorialSpringDamper.py (Ex), tutorialSpringDamperCreate.py (Ex), cartesianSpringDamper.py (Ex), coordinateSpringDamper.py (Ex)