pendulum2Dconstraint.py

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  1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  2# This is an EXUDYN example
  3#
  4# Details:  Mathematical pendulum with constraint;
  5#           Remark: update from pendulum.py example
  6#
  7# Author:   Johannes Gerstmayr
  8# Date:     2019-12-26
  9#
 10# 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.
 11#
 12#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 13
 14import exudyn as exu
 15from exudyn.utilities import *
 16
 17SC = exu.SystemContainer()
 18mbs = SC.AddSystem()
 19
 20L = 0.8 #distance
 21mass = 2.5
 22g = 9.81
 23
 24r = 0.05 #just for graphics
 25graphicsBackground = GraphicsDataRectangle(-1.2*L,-1.2*L, 1.2*L, 0.2*L, [1,1,1,1]) #for appropriate zoom
 26graphicsSphere = GraphicsDataSphere(point=[0,0,0], radius=r, color=[1.,0.2,0.2,1], nTiles = 16)
 27
 28#add ground object and mass point:
 29oGround = mbs.AddObject(ObjectGround(referencePosition = [0,0,0],
 30                           visualization = VObjectGround(graphicsData = [graphicsBackground])))
 31nMass = mbs.AddNode(NodePoint2D(referenceCoordinates=[L,0],
 32                                initialCoordinates=[0,0],
 33                                initialVelocities=[0,0]))
 34oMass = mbs.AddObject(MassPoint2D(physicsMass = mass, nodeNumber = nMass,
 35                                  visualization = VObjectMassPoint2D(graphicsData = [graphicsSphere])))
 36
 37mMass = mbs.AddMarker(MarkerNodePosition(nodeNumber=nMass))
 38mGround = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition = [0,0,0]))
 39oDistance = mbs.AddObject(DistanceConstraint(markerNumbers = [mGround, mMass], distance = L))
 40
 41#add loads:
 42mbs.AddLoad(Force(markerNumber = mMass, loadVector = [0, -mass*g, 0]))
 43
 44sDist = mbs.AddSensor(SensorObject(objectNumber=oDistance, storeInternal=True,
 45                                   outputVariableType=exu.OutputVariableType.Distance))
 46
 47#print(mbs)
 48
 49mbs.Assemble()
 50
 51simulationSettings = exu.SimulationSettings()
 52
 53f = 1000000
 54simulationSettings.timeIntegration.numberOfSteps = int(1*f)
 55simulationSettings.timeIntegration.endTime = 0.001*f
 56simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/5000
 57simulationSettings.solutionSettings.sensorsWritePeriod = simulationSettings.timeIntegration.endTime/50000
 58#simulationSettings.displayComputationTime = True
 59simulationSettings.timeIntegration.verboseMode = 1
 60simulationSettings.timeIntegration.verboseModeFile = 0
 61
 62#these Newton settings are slightly faster than full Newton:
 63simulationSettings.timeIntegration.newton.useModifiedNewton = True
 64simulationSettings.timeIntegration.newton.modifiedNewtonJacUpdatePerStep = True
 65
 66simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.60 #0.62 is approx. the limit
 67simulationSettings.timeIntegration.adaptiveStep = False
 68
 69simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations = True
 70simulationSettings.solutionSettings.coordinatesSolutionFileName= "coordinatesSolution.txt"
 71
 72simulationSettings.displayStatistics = True
 73#simulationSettings.solutionSettings.recordImagesInterval = 0.04
 74
 75SC.visualizationSettings.nodes.defaultSize = 0.05
 76exu.StartRenderer()
 77
 78#mbs.WaitForUserToContinue()
 79#exu.InfoStat()
 80mbs.SolveDynamic(simulationSettings,
 81                 # solverType=exu.DynamicSolverType.TrapezoidalIndex2
 82                 )
 83#exu.InfoStat()
 84
 85SC.WaitForRenderEngineStopFlag()
 86exu.StopRenderer() #safely close rendering window!
 87
 88nODE2 = len(mbs.systemData.GetODE2Coordinates())
 89print("ODE2=",nODE2)
 90
 91#plot constraint error:
 92
 93mbs.PlotSensor(sensorNumbers=sDist, offsets=[-L], closeAll=True)
 94
 95#old way, better use PlotSensor:
 96import matplotlib.pyplot as plt
 97import matplotlib.ticker as ticker
 98
 99#plot y-acceleration:
100data = np.loadtxt('coordinatesSolution.txt', comments='#', delimiter=',')
101plt.figure()
102plt.plot(data[:,0], data[:,1+2*nODE2+1], 'b-')
103
104ax=plt.gca() # get current axes
105ax.grid(True, 'major', 'both')
106ax.xaxis.set_major_locator(ticker.MaxNLocator(10))
107ax.yaxis.set_major_locator(ticker.MaxNLocator(10))
108plt.tight_layout()
109plt.show()