ObjectGenericODE1

A system of \(n\) ODE1, having a system matrix, a rhs vector, but mostly it will use a user function to describe special ODE1 systems. It is based on NodeGenericODE1 nodes. NOTE that all matrices, vectors, etc. must have the same dimensions \(n\) or \((n \times n)\), or they must be empty \((0 \times 0)\), using [] in Python.

Additional information for ObjectGenericODE1:

• This Object has/provides the following types = MultiNoded
• Requested Node type: read detailed information of item

The item ObjectGenericODE1 with type = ‘GenericODE1’ has the following parameters:

• name [type = String, default = ‘’]:

  objects’s unique name
• nodeNumbers [\(\mathbf{n}_n = [n_0,\,\ldots,\,n_n]\tp\), type = ArrayNodeIndex, default = []]:

  node numbers which provide the coordinates for the object (consecutively as provided in this list)
• systemMatrix [\({\mathbf{A}} \in \Rcal^{n \times n}\), type = NumpyMatrix, default = Matrix[]]:

  system matrix (state space matrix) of first order ODE
• rhsVector [\({\mathbf{f}} \in \Rcal^{n}\), type = NumpyVector, default = []]:

  a constant rhs vector (e.g., for constant input)
• rhsUserFunction [\({\mathbf{f}}_{user} \in \Rcal^{n}\), type = PyFunctionVectorMbsScalarIndexVector, default = 0]:

  A Python user function which computes the right-hand-side (rhs) of the first order ODE; see description below
• coordinateIndexPerNode [type = ArrayIndex, default = []]:

  this list contains the local coordinate index for every node, which is needed, e.g., for markers; the list is generated automatically every time parameters have been changed
• tempCoordinates [\({\mathbf{c}}_{temp} \in \Rcal^{n}\), type = NumpyVector, default = []]:

  temporary vector containing coordinates
• tempCoordinates_t [\(\dot {\mathbf{c}}_{temp} \in \Rcal^{n}\), type = NumpyVector, default = []]:

  temporary vector containing velocity coordinates
• visualization [type = VObjectGenericODE1]:

  parameters for visualization of item

The item VObjectGenericODE1 has the following parameters:

• show [type = Bool, default = True]:

  set true, if item is shown in visualization and false if it is not shown

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DESCRIPTION of ObjectGenericODE1

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

• Coordinates:

  all ODE1 coordinates
• Coordinates\_t:

  all ODE1 velocity coordinates

Equations of motion

An object with node numbers \([n_0,\,\ldots,\,n_n]\) and according numbers of nodal coordinates \([n_{c_0},\,\ldots,\,n_{c_n}]\), the total number of equations (=coordinates) of the object is

\[n = \sum_{i} n_{c_i},\]

which is used throughout the description of this object.

Equations of motion

(63)\[\dot {\mathbf{q}} = {\mathbf{f}} + {\mathbf{f}}_{user}(mbs, t, i_N, {\mathbf{q}})\]

Note that the user function \({\mathbf{f}}_{user}(mbs, t, i_N, {\mathbf{q}})\) may be empty (=0), and that iN represents the itemNumber (=objectNumber).

CoordinateLoads are added for the respective ODE1 coordinate on the RHS of the latter equation.

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Userfunction: rhsUserFunction(mbs, t, itemNumber, q)

A user function, which computes a RHS vector depending on current time and states of the object. Can be used to create any kind of first order system, especially state space equations (inputs are added via CoordinateLoads to every node). Note that itemNumber represents the index of the ObjectGenericODE1 object in mbs, which can be used to retrieve additional data from the object through mbs.GetObjectParameter(itemNumber, ...), see the according description of GetObjectParameter.

arguments / return	type or size	description
mbs	MainSystem	provides MainSystem mbs to which object belongs
t	Real	current time in mbs
itemNumber	Index	integer number \(i_N\) of the object in mbs, allowing easy access to all object data via mbs.GetObjectParameter(itemNumber, …)
q	Vector \(\in \Rcal^n\)	object coordinates (composed from ODE1 nodal coordinates) in current configuration, without reference values
returnValue	Vector \(\in \Rcal^{n}\)	returns force vector for object

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User function example:

A = numpy.diag([200,100])
#simple linear user function returning A*q + const
def UFrhs(mbs, t, itemNumber, q):
    return np.dot(A, q) + np.array([0,2])

nODE1 = mbs.AddNode(NodeGenericODE1(referenceCoordinates=[0,0],
                                    initialCoordinates=[1,0], numberOfODE1Coordinates=2))

#now add object instead of object in mini-example:
oGenericODE1 = mbs.AddObject(ObjectGenericODE1(nodeNumbers=[nODE1],
                   rhsUserFunction=UFrhs))

MINI EXAMPLE for ObjectGenericODE1

#set up a 2-DOF system
nODE1 = mbs.AddNode(NodeGenericODE1(referenceCoordinates=[0,0],
                                    initialCoordinates=[1,0],
                                    numberOfODE1Coordinates=2))

#build system matrix and force vector
#undamped mechanical system with m=1, K=100, f=1
A = np.array([[0,1],
              [-100,0]])
b = np.array([0,1])

oGenericODE1 = mbs.AddObject(ObjectGenericODE1(nodeNumbers=[nODE1],
                                               systemMatrix=A,
                                               rhsVector=b))

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

sims=exu.SimulationSettings()
solverType = exu.DynamicSolverType.RK44
mbs.SolveDynamic(solverType=solverType, simulationSettings=sims)

#check result at default integration time
exudynTestGlobals.testResult = mbs.GetNodeOutput(nODE1, exu.OutputVariableType.Coordinates)[0]

Relevant Examples and TestModels with weblink:

HydraulicsUserFunction.py (Examples/), lugreFrictionODE1.py (Examples/), lugreFrictionTest.py (Examples/), solverExplicitODE1ODE2test.py (TestModels/)

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