ObjectMass1D

A 1D (translational) mass which is attached to Node1D. Note, that the mass does not need to have the interpretation as a translational mass.

Interface

Python names: ObjectMass1D or Mass1D, and VMass1D for its visualization
Nodes it takes: Node1D, NodeGenericODE2, NodePointGround
Body markers that can be placed on it: MarkerBodyMass, MarkerBodyPosition, MarkerBodyRigid

Parameters

The parameters of the item; in a dictionary, its type is ‘Mass1D’:

name	type	size	default	description
name	String		‘’	objects’s unique name
mass	UReal		0.	(symbol: \(m\)) mass [SI:kg] of mass
nodeNumber	NodeIndex		invalid (-1)	(symbol: \(n0\)) node number (type NodeIndex) for Node1D
referencePosition	Vector3D	3	[0.,0.,0.]	(symbol: \(\LU{0}{\pRef_0}\)) a reference position, used to transform the 1D coordinate to a position
referenceRotation	Matrix3D	9	[[1,0,0], [0,1,0], [0,0,1]]	(symbol: \(\LU{0b}{\Rot_{0}} \in \Rcal^{3 \times 3}\)) the constant body rotation matrix, which transforms body-fixed (b) to global (0) coordinates
visualization	VObjectMass1D			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 VObjectMass1D, 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 along 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	\(\LU{0}{\pv}\cConfig\)	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		vector with 3 components of the Euler/Tait-Bryan angles in xyz-sequence (\(\LU{0b}{\Rot}\cConfig=:\Rot_0(\varphi_0) \cdot \Rot_1(\varphi_1) \cdot \Rot_2(\varphi_2)\)), recomputed from rotation matrix \(\LU{0b}{\Rot}\)
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	\(T = \frac{1}{2} m\, \dot q_0^2\)	kinetic energy of the mass; 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
position coordinate	\({p_0}\cConfig = {c_0}\cConfig + {c_0}\cRef\)	the coordinate \(c_0\) of the node plus its reference value
Position	\(\LU{0}{\pv}\cConfig = \LU{0}{\pRef_0} + \LU{0b}{\Rot_{0}} \LU{b}{\vr{p_0}{0}{0}}\cConfig\)	the mass moves along the local \(x\)-axis of the frame given by `referencePosition` \(\LU{0}{\pRef_0}\) and `referenceRotation` \(\LU{0b}{\Rot_{0}}\)
Velocity	\(\LU{0}{\vv}\cConfig = \LU{0b}{\Rot_{0}} \LU{b}{\vr{\dot c_0}{0}{0}}\cConfig\)	velocity of the mass
applied force	\(\LU{0}{\fv}_a\)	3D force from loads, connectors and joints
residual force	\(f\)	the component of the applied forces along the axis

The coordinate need not be a translation: the object is any scalar mass-spring-damper equation.

Equations of motion

\[ m \cdot \ddot c_0 = f , \quad f = \LU{b}{[1,\,0,\,0]} \LU{b0}{\Rot_{0}} \LU{0}{\fv}_a . \]

Marker interfaces

\[ \LU{0}{\Jm_{pos}} = \frac{\partial \LU{0}{\vv}}{\partial \dot c_0} = \LU{0b}{\Rot_{0}} \LU{b}{\vr{1}{0}{0}} , \quad \LU{0}{\Jm_{rot}} = \Null : \]

a force acts with its component along the axis, a torque has no effect. The mass-weighted Jacobian is \(m\) times \(\LU{0}{\Jm_{pos}}\).

Mini example

node = mbs.AddNode(Node1D(referenceCoordinates = [1], 
                          initialCoordinates=[0.5],
                          initialVelocities=[0.5]))
mass = mbs.AddObject(Mass1D(nodeNumber = node, mass=1))

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

#check result, get current mass position at local position [0,0,0]
exu.sys['testResult'] = mbs.GetObjectOutputBody(mass, exu.OutputVariableType.Position, [0,0,0])[0]
#final x-coordinate of position shall be 2

Relevant Examples (Ex) and TestModels (TM) with weblink to github: craneReevingSystem.py (Ex), lugreFrictionTest.py (Ex), mpi4pyExample.py (Ex), multiprocessingTest.py (Ex), nMassOscillator.py (Ex), nMassOscillatorEigenmodes.py (Ex), nMassOscillatorInteractive.py (Ex), connectorOutputVariablesTest.py (TM), contactComparisonTest.py (TM), coordinateSpringDamperExtVelocityOffsetTest.py (TM), energiesTest.py (TM), explicitSolversPostNewtonTest.py (TM), driveTrainTest.py (TM), mainSystemUserFunctionsTest.py (TM)