.. _testmodels-coordinatevectorconstraintgenericode2: **************************************** coordinateVectorConstraintGenericODE2.py **************************************** You can view and download this file on Github: `coordinateVectorConstraintGenericODE2.py `_ .. code-block:: python :linenos: #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ # This is an EXUDYN example # # Details: Example of double pendulum with Mass points: CoordinateVectorConstraint and GenericODE2 # # Author: Johannes Gerstmayr # Date: 2022-03-17 # # 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 import numpy as np useGraphics = True #without test #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel: try: #only if called from test suite from modelUnitTests import exudynTestGlobals #for globally storing test results useGraphics = exudynTestGlobals.useGraphics except: class ExudynTestGlobals: pass exudynTestGlobals = ExudynTestGlobals() #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ SC = exu.SystemContainer() mbs = SC.AddSystem() withUserFunction = True L = 0.8 #length of arm mass = 2.5 g = 9.81 r = 0.05 #just for graphics d = r/2 #add ground object and mass point: sizeRect = 1.2*L*2 #graphicsBackground = GraphicsDataRectangle(-sizeRect,-sizeRect, sizeRect, 0.2*L, [1,1,1,1]) #for appropriate zoom graphicsBackground = graphics.CheckerBoard(point=[0,-0.5*sizeRect,-2*r],size=sizeRect*1.8) oGround = mbs.AddObject(ObjectGround(referencePosition = [0,0,0], visualization = VObjectGround(graphicsData = [graphicsBackground]))) graphicsSphere = graphics.Sphere(point=[0,0,0], radius=r, color=graphics.color.steelblue, nTiles = 16) nR0 = mbs.AddNode(Point2D(referenceCoordinates=[L,0])) mGround0 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition = [0,0,0])) mTip0 = mbs.AddMarker(MarkerNodePosition(nodeNumber=nR0)) if not withUserFunction: #with internal terms: oCD0 = mbs.AddObject(DistanceConstraint(markerNumbers=[mGround0, mTip0], distance=L)) else: #just for drawing, with inactive connector: oCD0 = mbs.AddObject(DistanceConstraint(markerNumbers=[mGround0, mTip0], distance=L, activeConnector=False)) # mbs.AddLoad(Force(markerNumber = mTip0, loadVector = [0, -mass*g, 0])) fileNameDouble = 'solution/coordVecConstraintRefDouble.txt' sPos0 = mbs.AddSensor(SensorNode(nodeNumber = nR0, storeInternal = True, outputVariableType=exu.OutputVariableType.Position)) graphicsSphere = graphics.Sphere(point=[0,0,0], radius=r, color=graphics.color.red, nTiles = 16) nR1 = mbs.AddNode(Point2D(referenceCoordinates=[L*2,0])) #instead of MassPoint2D, create one object ... oGeneric = mbs.AddObject(ObjectGenericODE2(nodeNumbers=[nR0, nR1], massMatrix=mass*np.eye(4))) mTip1 = mbs.AddMarker(MarkerNodePosition(nodeNumber=nR1)) if not withUserFunction: #with internal terms: oCD1 = mbs.AddObject(DistanceConstraint(markerNumbers=[mTip0, mTip1], distance=L)) else: #just for drawing, with inactive connector: mbs.AddObject(DistanceConstraint(markerNumbers=[mTip0, mTip1], distance=L, activeConnector=False)) nGround = mbs.AddNode(NodePointGround()) mCoordsGround = mbs.AddMarker(MarkerNodeCoordinates(nodeNumber=nGround)) mCoords0 = mbs.AddMarker(MarkerNodeCoordinates(nodeNumber=nR0)) mCoords1 = mbs.AddMarker(MarkerNodeCoordinates(nodeNumber=nR1)) mCoordsAll = mbs.AddMarker(MarkerObjectODE2Coordinates(objectNumber=oGeneric)) def UFconstraint(mbs, t, itemNumber, q, q_t,velocityLevel): #print("q=", q, ", q_t=", q_t) return [np.sqrt(q[0]**2 + q[1]**2) - L, np.sqrt((q[2]-q[0])**2 + (q[3]-q[1])**2) - L] def UFjacobian(mbs, t, itemNumber, q, q_t,velocityLevel): #print("q=", q, ", q_t=", q_t) jac = np.zeros((2,4)) f0 = np.sqrt(q[0]**2 + q[1]**2) jac[0,0] = q[0]/f0 jac[0,1] = q[1]/f0 f1 = np.sqrt((q[2]-q[0])**2 + (q[3]-q[1])**2) jac[1,0] =-(q[2]-q[0])/f1 jac[1,1] =-(q[3]-q[1])/f1 jac[1,2] = (q[2]-q[0])/f1 jac[1,3] = (q[3]-q[1])/f1 return jac mbs.AddObject(CoordinateVectorConstraint(markerNumbers=[mCoordsGround, mCoordsAll], #markerNumbers=[mCoords0, mCoords1], #ALTERNATIVELY: with markers on nodes (but only works for max. 2 nodes!) scalingMarker0=np.zeros((2,4)), #needed to define number of algebraic equations; rows=nAE, cols=len(q) of mCoordsGround + mCoords0 constraintUserFunction=UFconstraint, jacobianUserFunction=UFjacobian, visualization=VCoordinateVectorConstraint(show=False))) #q mbs.AddLoad(Force(markerNumber = mTip1, loadVector = [0, -mass*g, 0])) sPos1 = mbs.AddSensor(SensorNode(nodeNumber = nR1, storeInternal = True, #fileName=fileNameDouble, outputVariableType=exu.OutputVariableType.Position)) mbs.Assemble() simulationSettings = exu.SimulationSettings() #useGraphics=False tEnd = 1 h = 1e-3 if useGraphics: tEnd = 1 simulationSettings.timeIntegration.simulateInRealtime = True simulationSettings.timeIntegration.realtimeFactor = 1 simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h) simulationSettings.timeIntegration.endTime = tEnd #simulationSettings.solutionSettings.solutionWritePeriod = h simulationSettings.timeIntegration.verboseMode = 1 #simulationSettings.solutionSettings.solutionWritePeriod = tEnd/steps simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.8 #SHOULD work with 0.9 as well SC.visualizationSettings.nodes.showBasis=True SC.visualizationSettings.nodes.drawNodesAsPoint=False SC.visualizationSettings.nodes.defaultSize=r if useGraphics: exu.StartRenderer() mbs.WaitForUserToContinue() mbs.SolveDynamic(simulationSettings) p0=mbs.GetNodeOutput(nR0, exu.OutputVariableType.Position) exu.Print("p0=", list(p0)) u=sum(p0) exu.Print('solution of coordinateVectorConstraint=',u) exudynTestGlobals.testError = u - (-1.0825265797698322) exudynTestGlobals.testResult = u #%%++++++++++++++++++++++++++++ if useGraphics: SC.WaitForRenderEngineStopFlag() exu.StopRenderer() #safely close rendering window! from exudyn.plot import PlotSensorDefaults PlotSensorDefaults().fontSize = 12 # PlotSensorDefaults().markerStyles=['x','o ','v ','^ ','s '] # mbs.PlotSensor([sPos0,sPos0,sPos1,sPos1], components=[0,1,0,1], closeAll=True) #if reference solution computed: mbs.PlotSensor([sPos0,sPos0,sPos1,sPos1,fileNameDouble], components=[0,1,0,1,1], closeAll=True, markerStyles=['','','','','x'], lineStyles=['-','-','-','-',''])