.. _examples-pendulum2dconstraint:

***********************
pendulum2Dconstraint.py
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You can view and download this file on Github: `pendulum2Dconstraint.py <https://github.com/jgerstmayr/EXUDYN/tree/master/main/pythonDev/Examples/pendulum2Dconstraint.py>`_

.. code-block:: python
   :linenos:

   #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
   # This is an EXUDYN example
   #
   # Details:  Mathematical pendulum with constraint;
   #           Remark: update from pendulum.py example
   #
   # Author:   Johannes Gerstmayr
   # Date:     2019-12-26
   #
   # Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
   #
   #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
   
   import exudyn as exu
   from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities
   import exudyn.graphics as graphics #only import if it does not conflict
   
   SC = exu.SystemContainer()
   mbs = SC.AddSystem()
   
   L = 0.8 #distance
   mass = 2.5
   g = 9.81
   
   r = 0.05 #just for graphics
   graphicsBackground = GraphicsDataRectangle(-1.2*L,-1.2*L, 1.2*L, 0.2*L, [1,1,1,1]) #for appropriate zoom
   graphicsSphere = graphics.Sphere(point=[0,0,0], radius=r, color=[1.,0.2,0.2,1], nTiles = 16)
   
   #add ground object and mass point:
   oGround = mbs.AddObject(ObjectGround(referencePosition = [0,0,0], 
                              visualization = VObjectGround(graphicsData = [graphicsBackground])))
   nMass = mbs.AddNode(NodePoint2D(referenceCoordinates=[L,0], 
                                   initialCoordinates=[0,0],
                                   initialVelocities=[0,0]))
   oMass = mbs.AddObject(MassPoint2D(physicsMass = mass, nodeNumber = nMass, 
                                     visualization = VObjectMassPoint2D(graphicsData = [graphicsSphere])))
   
   mMass = mbs.AddMarker(MarkerNodePosition(nodeNumber=nMass))
   mGround = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition = [0,0,0]))
   oDistance = mbs.AddObject(DistanceConstraint(markerNumbers = [mGround, mMass], distance = L))
   
   #add loads:
   mbs.AddLoad(Force(markerNumber = mMass, loadVector = [0, -mass*g, 0])) 
   
   sDist = mbs.AddSensor(SensorObject(objectNumber=oDistance, storeInternal=True, 
                                      outputVariableType=exu.OutputVariableType.Distance))
   
   #print(mbs)
   
   mbs.Assemble()
   
   simulationSettings = exu.SimulationSettings()
   
   f = 1000000
   simulationSettings.timeIntegration.numberOfSteps = int(1*f)
   simulationSettings.timeIntegration.endTime = 0.001*f
   simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/5000
   simulationSettings.solutionSettings.sensorsWritePeriod = simulationSettings.timeIntegration.endTime/50000
   #simulationSettings.displayComputationTime = True
   simulationSettings.timeIntegration.verboseMode = 1
   simulationSettings.timeIntegration.verboseModeFile = 0
   
   #these Newton settings are slightly faster than full Newton:
   simulationSettings.timeIntegration.newton.useModifiedNewton = True
   simulationSettings.timeIntegration.newton.modifiedNewtonJacUpdatePerStep = True
   
   simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.60 #0.62 is approx. the limit
   simulationSettings.timeIntegration.adaptiveStep = False
   
   simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations = True
   simulationSettings.solutionSettings.coordinatesSolutionFileName= "coordinatesSolution.txt"
   
   simulationSettings.displayStatistics = True
   #simulationSettings.solutionSettings.recordImagesInterval = 0.04
   
   SC.visualizationSettings.nodes.defaultSize = 0.05
   exu.StartRenderer()
   
   #mbs.WaitForUserToContinue()
   #exu.InfoStat()
   mbs.SolveDynamic(simulationSettings, 
                    # solverType=exu.DynamicSolverType.TrapezoidalIndex2
                    )
   #exu.InfoStat()
   
   SC.WaitForRenderEngineStopFlag()
   exu.StopRenderer() #safely close rendering window!
   
   nODE2 = len(mbs.systemData.GetODE2Coordinates())
   print("ODE2=",nODE2)
   
   #plot constraint error:
   
   mbs.PlotSensor(sensorNumbers=sDist, offsets=[-L], closeAll=True)
   
   #old way, better use PlotSensor:
   import matplotlib.pyplot as plt
   import matplotlib.ticker as ticker
   
   #plot y-acceleration:
   data = np.loadtxt('coordinatesSolution.txt', comments='#', delimiter=',')
   plt.figure()
   plt.plot(data[:,0], data[:,1+2*nODE2+1], 'b-')
   
   ax=plt.gca() # get current axes
   ax.grid(True, 'major', 'both')
   ax.xaxis.set_major_locator(ticker.MaxNLocator(10)) 
   ax.yaxis.set_major_locator(ticker.MaxNLocator(10)) 
   plt.tight_layout()
   plt.show()