coordinateVectorConstraint.py
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1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2# This is an EXUDYN example
3#
4# Details: Example of double pendulum with Mass points and CoordinateVectorConstraint;
5#
6# Author: Johannes Gerstmayr
7# Date: 2022-03-17
8#
9# 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.
10#
11#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
12
13import exudyn as exu
14from exudyn.utilities import *
15import numpy as np
16
17useGraphics = True #without test
18#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
19#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
20try: #only if called from test suite
21 from modelUnitTests import exudynTestGlobals #for globally storing test results
22 useGraphics = exudynTestGlobals.useGraphics
23except:
24 class ExudynTestGlobals:
25 pass
26 exudynTestGlobals = ExudynTestGlobals()
27#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
28
29SC = exu.SystemContainer()
30mbs = SC.AddSystem()
31
32doublePendulum = True
33withUserFunction = True
34
35L = 0.8 #length of arm
36mass = 2.5
37g = 9.81
38
39r = 0.05 #just for graphics
40d = r/2
41
42#add ground object and mass point:
43sizeRect = 1.2*L*(1+int(doublePendulum))
44#graphicsBackground = GraphicsDataRectangle(-sizeRect,-sizeRect, sizeRect, 0.2*L, [1,1,1,1]) #for appropriate zoom
45graphicsBackground = GraphicsDataCheckerBoard(point=[0,-0.5*sizeRect,-2*r],size=sizeRect*1.8)
46
47oGround = mbs.AddObject(ObjectGround(referencePosition = [0,0,0],
48 visualization = VObjectGround(graphicsData = [graphicsBackground])))
49
50
51graphicsSphere = GraphicsDataSphere(point=[0,0,0], radius=r, color=color4steelblue, nTiles = 16)
52
53nR0 = mbs.AddNode(Point2D(referenceCoordinates=[L,0]))
54oR0 = mbs.AddObject(MassPoint2D(nodeNumber=nR0, physicsMass=mass, visualization=VMassPoint2D(graphicsData=[graphicsSphere])))
55
56mGround0 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition = [0,0,0]))
57mTip0 = mbs.AddMarker(MarkerNodePosition(nodeNumber=nR0))
58
59if not withUserFunction: #with internal terms:
60 oCD0 = mbs.AddObject(DistanceConstraint(markerNumbers=[mGround0, mTip0], distance=L))
61else:
62 #just for drawing, with inactive connector:
63 mbs.AddObject(DistanceConstraint(markerNumbers=[mGround0, mTip0], distance=L, activeConnector=False))
64
65 nGround = mbs.AddNode(NodePointGround())
66 mCoordsGround = mbs.AddMarker(MarkerNodeCoordinates(nodeNumber=nGround))
67 mCoords0 = mbs.AddMarker(MarkerNodeCoordinates(nodeNumber=nR0))
68
69 #constraint user function:
70 def UFconstraint(mbs, t, itemNumber, q, q_t,velocityLevel):
71 #print("q=", q, ", q_t=", q_t)
72 return [np.sqrt(q[0]**2 + q[1]**2) - L]
73
74 #constraint jacobian user function:
75 def UFjacobian(mbs, t, itemNumber, q, q_t,velocityLevel):
76 #print("q=", q, ", q_t=", q_t)
77 jac = np.zeros((1,2))
78
79 f = np.sqrt(q[0]**2 + q[1]**2)
80 jac[0,0] = q[0]/f
81 jac[0,1] = q[1]/f
82 return jac
83
84 mbs.AddObject(CoordinateVectorConstraint(markerNumbers=[mCoordsGround, mCoords0],
85 scalingMarker0=np.zeros((1,2)), #needed to define number of algebraic equations; rows=nAE, cols=len(q) of mCoordsGround + mCoords0
86 constraintUserFunction=UFconstraint,
87 jacobianUserFunction=UFjacobian,
88 visualization=VCoordinateVectorConstraint(show=False)))
89
90#
91mbs.AddLoad(Force(markerNumber = mTip0, loadVector = [0, -mass*g, 0]))
92
93fileNameDouble = 'solution/coordVecConstraintRefDouble.txt'
94fileNameSingle = 'solution/coordVecConstraintRefSingle.txt'
95
96sPos0 = mbs.AddSensor(SensorNode(nodeNumber = nR0, storeInternal = True,
97 #fileName=fileNameSingle, #single pendulum
98 outputVariableType=exu.OutputVariableType.Position))
99
100
101#for double pendulum, we add a second link
102if doublePendulum:
103 graphicsSphere = GraphicsDataSphere(point=[0,0,0], radius=r, color=color4red, nTiles = 16)
104 nR1 = mbs.AddNode(Point2D(referenceCoordinates=[L*2,0]))
105 oR1 = mbs.AddObject(MassPoint2D(nodeNumber=nR1, physicsMass=mass, visualization=VMassPoint2D(graphicsData=[graphicsSphere])))
106
107 mTip1 = mbs.AddMarker(MarkerNodePosition(nodeNumber=nR1))
108
109 if not withUserFunction: #with internal terms:
110 oCD1 = mbs.AddObject(DistanceConstraint(markerNumbers=[mTip0, mTip1], distance=L))
111 else:
112 #just for drawing, with inactive connector:
113 mbs.AddObject(DistanceConstraint(markerNumbers=[mTip0, mTip1], distance=L, activeConnector=False))
114
115 mCoords0 = mbs.AddMarker(MarkerNodeCoordinates(nodeNumber=nR0))
116 mCoords1 = mbs.AddMarker(MarkerNodeCoordinates(nodeNumber=nR1))
117
118 #constraint user function:
119 def UFconstraint2(mbs, t, itemNumber, q, q_t,velocityLevel):
120 #print("q=", q, ", q_t=", q_t)
121 return [np.sqrt((q[2]-q[0])**2 + (q[3]-q[1])**2) - L]
122
123 #constraint jacobian user function:
124 def UFjacobian2(mbs, t, itemNumber, q, q_t,velocityLevel):
125 #print("q=", q, ", q_t=", q_t)
126 jac = np.zeros((1,4))
127 f = np.sqrt((q[2]-q[0])**2 + (q[3]-q[1])**2)
128 jac[0,0] =-(q[2]-q[0])/f
129 jac[0,1] =-(q[3]-q[1])/f
130 jac[0,2] = (q[2]-q[0])/f
131 jac[0,3] = (q[3]-q[1])/f
132 return jac
133
134 mbs.AddObject(CoordinateVectorConstraint(markerNumbers=[mCoords0, mCoords1],
135 scalingMarker0=np.zeros((1,2+2)), #needed to define number of algebraic equations; rows=nAE, cols=len(q) of mCoordsGround + mCoords0
136 constraintUserFunction=UFconstraint2,
137 jacobianUserFunction=UFjacobian2,
138 visualization=VCoordinateVectorConstraint(show=False)))
139
140
141 #
142 mbs.AddLoad(Force(markerNumber = mTip1, loadVector = [0, -mass*g, 0]))
143
144 sPos1 = mbs.AddSensor(SensorNode(nodeNumber = nR1, storeInternal = True,
145 #fileName=fileNameDouble,
146 outputVariableType=exu.OutputVariableType.Position))
147
148
149
150mbs.Assemble()
151
152simulationSettings = exu.SimulationSettings()
153
154# useGraphics=False
155tEnd = 1
156h = 1e-3
157if useGraphics:
158 tEnd = 1
159 simulationSettings.timeIntegration.simulateInRealtime = True
160 simulationSettings.timeIntegration.realtimeFactor = 3
161
162simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
163simulationSettings.timeIntegration.endTime = tEnd
164
165#simulationSettings.solutionSettings.solutionWritePeriod = h
166simulationSettings.timeIntegration.verboseMode = 1
167#simulationSettings.solutionSettings.solutionWritePeriod = tEnd/steps
168
169simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.8 #SHOULD work with 0.9 as well
170
171SC.visualizationSettings.nodes.showBasis=True
172
173if useGraphics:
174 exu.StartRenderer()
175 mbs.WaitForUserToContinue()
176
177mbs.SolveDynamic(simulationSettings)
178
179p0=mbs.GetObjectOutputBody(oR0, exu.OutputVariableType.Position, localPosition=[0,0,0])
180exu.Print("p0=", list(p0))
181u=sum(p0)
182
183exu.Print('solution of coordinateVectorConstraint=',u)
184
185exudynTestGlobals.testError = u - (-1.0825265797698322)
186exudynTestGlobals.testResult = u
187
188
189if useGraphics:
190 SC.WaitForRenderEngineStopFlag()
191 exu.StopRenderer() #safely close rendering window!
192
193 if doublePendulum:
194 mbs.PlotSensor([sPos0,sPos0,sPos1,sPos1], components=[0,1,0,1], closeAll=True)
195 else:
196 mbs.PlotSensor([sPos0,sPos0], components=[0,1], closeAll=True)