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(testmodels-initialaccelerationstest)=
# initialAccelerationsTest.py

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

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

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  The initial accelerations of the generalized-alpha method, timeIntegration.generalizedAlpha.
#           computeInitialAccelerations (#2235): a pendulum - a mass point on a distance constraint of length
#           L - starts horizontally with velocity v perpendicular to the rod. Its initial acceleration is the
#           centripetal v^2/L towards the pivot plus gravity; the term of the initial velocity comes from the
#           derivative of the constraint Jacobian, and the multiplier is the rod force m v^2/L. Without
#           computeInitialAccelerations the accelerations are zero.
#
# Author:   Johannes Gerstmayr
# Date:     2026-10-05
#
# 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)

L = 0.8
v = 1.5
g = 9.81

def InitialAccelerations(computeInitialAccelerations, linearSolverType=exu.LinearSolverType.EXUdense):
    SC = exu.SystemContainer()
    mbs = SC.AddSystem()
    oGround = mbs.CreateGround()
    oMass = mbs.CreateMassPoint(referencePosition=[L,0,0], initialVelocity=[0,v,0], mass=2, gravity=[0,-g,0])
    mbs.CreateDistanceConstraint(itemNumbers=[oGround, oMass])
    mbs.Assemble()
    settings = exu.SimulationSettings()
    settings.linearSolver.solverType = linearSolverType
    settings.solution.file.write = False
    settings.timeIntegration.verboseMode = 0
    settings.timeIntegration.generalizedAlpha.computeInitialAccelerations = computeInitialAccelerations
    solver = exu.MainSolverImplicitSecondOrder()
    solver.InitializeSolver(mbs, settings)
    return (mbs.systemData.GetODE2Coordinates_tt(), mbs.systemData.GetAECoordinates())

expected = np.array([-v**2/L, -g, 0])
u = 0
for linearSolverType in [exu.LinearSolverType.EXUdense, exu.LinearSolverType.EigenSparse]:
    (a, multipliers) = InitialAccelerations(True, linearSolverType)
    exu.Print(linearSolverType, ': initial accelerations', a, ', expected', expected, ', multiplier', multipliers)
    u += int(np.linalg.norm(a - expected) < 1e-8) + int(abs(abs(multipliers[0]) - 2*v**2/L) < 1e-8) + a[0] + 0.1*a[1]
(a, multipliers) = InitialAccelerations(False)
exu.Print('without computeInitialAccelerations:', a)
u += int(np.linalg.norm(a) == 0)

exu.Print('solution of initialAccelerationsTest=', u)

exu.sys['testResult'] = u
```