ObjectMassPoint2D

A 2D mass point which is attached to a position-based 2D node.

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

Interface

• Python names: ObjectMassPoint2D or MassPoint2D, and VMassPoint2D for its visualization

• Nodes it takes: NodePoint2D, NodeRigidBody2D, NodePoint2DSlope1, NodePointGround

• Body markers that can be placed on it: MarkerBodyMass, MarkerBodyPosition

Parameters

The parameters of the item; in a dictionary, its type is ‘MassPoint2D’:

name	type	size	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	VObjectMassPoint2D			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 VObjectMassPoint2D, 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	\(\LU{0}{\pv}\cConfig(\pLocB) = \LU{0}{\pRef}\cConfig + \LU{0}{\pRef}\cRef + \LU{0b}{\ImTwo}\pLocB\)	global position vector of translated local position; local (body) coordinate system = global coordinate system
Displacement	\(\LU{0}{\uv}\cConfig = [q_0,\;q_1,\;0]\cConfig\tp\)	global displacement vector of mass point
Velocity	\(\LU{0}{\vv}\cConfig = \LU{0}{\dot\uv}\cConfig = [\dot q_0,\;\dot q_1,\;0]\cConfig\tp\)	global velocity vector of mass point
Acceleration	\(\LU{0}{\av}\cConfig = \LU{0}{\ddot\uv}\cConfig = [\ddot q_0,\;\ddot q_1,\;0]\cConfig\tp\)	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	\(\LU{0}{\uv}\cConfig = [q_0,\;q_1,\;0]\cConfig\tp\)	displacement of the mass point in the \(x\)-\(y\) plane
node velocity	\(\LU{0}{\vv}\cConfig = [\dot q_0,\;\dot q_1,\;0]\cConfig\tp\)	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; \(f_2\) has no effect

Equations of motion

\[ \mp{m}{0} {0}{m} \vp{\ddot q_0}{\ddot q_1} = \vp{f_0}{f_1} . \]

Marker interfaces

The position Jacobian takes the \(x\) and \(y\) components of a global force,

\[\begin{split} \LU{0}{\Jm_{pos}} = \frac{\partial \LU{0}{\vv}}{\partial \dot\qv} = \left[\!\! \begin{array}{cc} 1 & 0 \\ 0 & 1 \\ 0 & 0 \end{array} \!\!\right] , \end{split}\]

so \(\Qm = \LU{0}{\Jm_{pos}}\tp \LU{0}{\fv}_a = [f_0,\;f_1]\tp\). There is no rotation Jacobian.

Mini example

node = mbs.AddNode(NodePoint2D(referenceCoordinates = [1,1], 
                             initialCoordinates=[0.5,0],
                             initialVelocities=[0.5,0]))
mbs.AddObject(MassPoint2D(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), tutorialSpringDamperCreate.py (Ex), pendulum2Dconstraint.py (Ex), cartesianSpringDamper.py (Ex), SliderCrank.py (Ex)