.. _examples-pendulum:

***********
pendulum.py
***********

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

.. code-block:: python
   :linenos:

   #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
   # This is an EXUDYN example
   #
   # Details:  Mathematical pendulum with constraint or spring-damper;
   #           Remark: uses old style definition of items
   #
   # Author:   Johannes Gerstmayr
   # Date:     2019-08-15
   #
   # 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
   
   import time #for sleep()
   SC = exu.SystemContainer()
   mbs = SC.AddSystem()
   
   nBodies = 2
   
   L = 0.8 #distance
   
   
   #phi = -0.7853981633974483 #-np.pi/8*2
   n1=mbs.AddNode({'nodeType': 'Point',
                   'referenceCoordinates': [L,0,0],
                   'initialCoordinates':   [0,0,0]})
                   #'initialCoordinates':   [-0.23431457505076192, -0.565685424949238, 0]})
                   #'initialCoordinates':   [-(L-L*np.cos(phi)),L*np.sin(phi),0]})
   
   Lo=L*0.3 #graphics
   mass = 2.5
   g = 9.81
   graphics1 = {'type':'Line', 'color':[0.1,0.1,0.8,1], 'data':[-(L+Lo),-(L+Lo),0, (L+Lo),-(L+Lo),0, (L+Lo),Lo,0, -(L+Lo),Lo,0, -(L+Lo),-(L+Lo), 0]} #background
   
   #add mass points and ground object:
   mbs.AddObject({'objectType': 'Ground', 'referencePosition': [0,0,0], 'VgraphicsData': [graphics1]})
   mbs.AddObject({'objectType': 'MassPoint', 'physicsMass': mass, 'nodeNumber': n1, 'VdrawSize':0.05*L}) 
   
   #add markers (needed for connectors and loads):
   for i in range(nBodies): mbs.AddMarker({'markerType': 'BodyPosition',  'bodyNumber': i,  'localPosition': [0.0, 0.0, 0.0], 'bodyFixed': False})
   
   k = 4000 #spring stiffness
   d = 200  #damping coefficient
   
   useConstraint = False
   if useConstraint:
       mbs.AddObject({'objectType': 'ConnectorDistance', 
                      'distance': L, 
                      'markerNumbers': [0,1], 
                      'drawSize': 0.01,
                      'color': [1,0,0,1]})
   else:
       mbs.AddObject({'objectType': 'ConnectorSpringDamper', 
                      'stiffness': k, 
                      'damping': d, 
                      'force': 0, 
                      'referenceLength':L, 
                      'markerNumbers': [0,1], 
                      'drawSize': 0.05})
   #add loads:
   #mbs.AddLoad({'loadType': 'ForceVector',  'markerNumber': nBodies-1,  'loadVector': [0, 20, 0]}) #gives 20N tension in Distance constraint
   mbs.AddLoad({'loadType': 'ForceVector',  'markerNumber': nBodies-1,  'loadVector': [0, -mass*g, 0]}) #gives approx. 0.001 deformation in x-direction
   
   print(mbs)
   
   mbs.Assemble()
   exu.StartRenderer()
   
   #time.sleep(10)
   
   simulationSettings = exu.SimulationSettings()
   
   computeDynamic = True
   if computeDynamic:
       f = 4400000
       simulationSettings.timeIntegration.numberOfSteps = 1*f
       simulationSettings.timeIntegration.endTime = 0.005*f
       simulationSettings.solutionSettings.writeSolutionToFile = True
       simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/5000
       simulationSettings.displayComputationTime = True
       simulationSettings.timeIntegration.verboseMode = 1
   
       simulationSettings.timeIntegration.newton.relativeTolerance = 1e-8
       simulationSettings.timeIntegration.newton.absoluteTolerance = 1e-10
       simulationSettings.timeIntegration.newton.useModifiedNewton = False
       simulationSettings.timeIntegration.newton.numericalDifferentiation.minimumCoordinateSize = 1
       simulationSettings.timeIntegration.newton.numericalDifferentiation.relativeEpsilon = 6.055454452393343e-06 #eps^(1/3)
       # simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
       simulationSettings.displayStatistics = True
   
       SC.visualizationSettings.nodes.showNumbers = True
       SC.visualizationSettings.bodies.showNumbers = True
       #mbs.visualizationSettings.connectors.showNumbers = True
       SC.visualizationSettings.nodes.defaultSize = 0.05
   
       exu.InfoStat()
       mbs.SolveDynamic(simulationSettings, 
                        solverType=exu.DynamicSolverType.TrapezoidalIndex2)
       exu.InfoStat()
   
   else:
       simulationSettings.solutionSettings.coordinatesSolutionFileName = "staticSolution.txt"
       simulationSettings.solutionSettings.appendToFile = False
       simulationSettings.staticSolver.newton.numericalDifferentiation.relativeEpsilon = 1e-4
       #simulationSettings.staticSolver.newton.relativeTolerance = 1e-6
       simulationSettings.staticSolver.newton.absoluteTolerance = 1e-1
       simulationSettings.staticSolver.verboseMode = 2
       #simulationSettings.staticSolver.newton.maxIterations = 5
   
       SC.visualizationSettings.nodes.showNumbers = True
       SC.visualizationSettings.bodies.showNumbers = True
       SC.visualizationSettings.connectors.showNumbers = True
       SC.visualizationSettings.nodes.defaultSize = 0.05
   
       mbs.SolveStatic(simulationSettings)
   
   #time.sleep(0.5)
   
   SC.WaitForRenderEngineStopFlag()
   exu.StopRenderer() #safely close rendering window!