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(testmodels-contactcurvecirclesfrictiontest)=
# contactCurveCirclesFrictionTest.py

You can view and download this file on Github: [contactCurveCirclesFrictionTest.py](https://github.com/jgerstmayr/EXUDYN/tree/master/python/TestModels/contactCurveCirclesFrictionTest.py)

```{code-block} python
:linenos:

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  ObjectContactCurveCircles with friction and its output variables (#2867): a circle (a planar rigid body)
#           slides along a straight curve under gravity with an initial velocity; the friction force mu*|f_N|
#           decelerates it by mu*g, so after the time t its velocity is v0 - mu*g*t. The output variables per
#           segment: DisplacementLocal the gap (the static penetration m*g/(k*l) for contactModel 0, with the
#           length l of the segment), VelocityLocal its rate, ForceLocal the force on the circle, [-mu*m*g, m*g]
#           while it slides.
#
# Author:   Johannes Gerstmayr
# Date:     2026-10-07
#
# 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 numpy as np

testIsActive = exu.sys.get('testIsActive', False)

mass, g, mu, v0 = 1., 10., 0.2, 1.
k, d, lSegment, radius = 1e5, 400., 4., 0.1
tEnd = 0.3

SC = exu.SystemContainer()
mbs = SC.AddSystem()
oGround = mbs.AddObject(ObjectGround())
gapStatic = mass*g/(k*lSegment)
node = mbs.AddNode(NodeRigidBody2D(referenceCoordinates=[0, radius - gapStatic, 0], initialVelocities=[v0, 0, 0]))
oBody = mbs.AddObject(ObjectRigidBody2D(nodeNumber=node, mass=mass, inertia=0.01))
mCircle = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oBody))
mbs.AddLoad(LoadForceVector(markerNumber=mCircle, loadVector=[0, -mass*g, 0]))
mCurve = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround))
segments = np.array([[2,0, -2,0]]) #one segment of length 4; the contact side is y > 0
nData = mbs.AddNode(NodeGenericData(numberOfDataCoordinates=3, initialCoordinates=[-1,0,0]))
oContact = mbs.AddObject(ObjectContactCurveCircles(markerNumbers=[mCurve, mCircle], nodeNumber=nData, circlesRadii=[radius],
                                                   segmentsData=exu.MatrixContainer(segments),
                                                   contactStiffness=k, contactDamping=d,
                                                   dynamicFriction=mu, frictionProportionalZone=1e-4))
mbs.Assemble()

simulationSettings = exu.SimulationSettings()
simulationSettings.timeIntegration.numberOfSteps = 3000
simulationSettings.timeIntegration.endTime = tEnd
simulationSettings.timeIntegration.verboseMode = 0
simulationSettings.solution.file.write = False
mbs.SolveDynamic(simulationSettings)

velocity = mbs.GetNodeOutput(node, exu.OutputVariableType.Velocity)
gap = np.atleast_1d(mbs.GetObjectOutput(oContact, exu.OutputVariableType.DisplacementLocal)) #one value per segment
gap_t = np.atleast_1d(mbs.GetObjectOutput(oContact, exu.OutputVariableType.VelocityLocal))
force = mbs.GetObjectOutput(oContact, exu.OutputVariableType.ForceLocal)
exu.Print('velocity', velocity[0], ', expected', v0 - mu*g*tEnd)
exu.Print('gap', gap, ', expected', -gapStatic, '; gap_t', gap_t)
exu.Print('force on the circle', force, ', expected', [-mu*mass*g, mass*g])

errors = (int(abs(velocity[0] - (v0 - mu*g*tEnd)) > 1e-3) + int(abs(gap[0] + gapStatic) > 1e-6)
          + int(abs(gap_t[0]) > 1e-3) + int(np.abs(force - [-mu*mass*g, mass*g]).max() > 1e-2))
exu.Print('contactCurveCirclesFrictionTest: errors', errors)
u = errors + velocity[0] + force[0] + force[1]
exu.Print('solution of contactCurveCirclesFrictionTest=', u)
exu.sys['testResult'] = u
```