Apps.PendulumMotion History

Hide minor edits - Show changes to markup

December 27, 2011, at 07:35 AM by 69.169.188.228 -
Changed lines 42-43 from:
to:
December 21, 2011, at 11:47 PM by 69.169.188.228 -
Changed lines 37-38 from:
  • (:html:)<a href="/online/plot.php?d=pendulum&f=pend.x.xml">Vertical Motion</a>(:htmlend:)
  • (:html:)<a href="/online/plot.php?d=pendulum&f=pend.y.xml">Horizontal Motion</a>(:htmlend:)
to:
  • (:html:)<a href="/online/plot.php?d=pendulum&f=pend3.x.xml">Vertical Motion</a>(:htmlend:)
  • (:html:)<a href="/online/plot.php?d=pendulum&f=pend3.y.xml">Horizontal Motion</a>(:htmlend:)
December 21, 2011, at 11:47 PM by 69.169.188.228 -
Changed lines 37-38 from:
  • (:html:)<a href="/online/plot.php?d=pendulum&f=SV(1).xml">Vertical Motion</a>(:htmlend:)
  • (:html:)<a href="/online/plot.php?d=pendulum&f=SV(2).xml">Horizontal Motion</a>(:htmlend:)
to:
  • (:html:)<a href="/online/plot.php?d=pendulum&f=pend.x.xml">Vertical Motion</a>(:htmlend:)
  • (:html:)<a href="/online/plot.php?d=pendulum&f=pend.y.xml">Horizontal Motion</a>(:htmlend:)
March 16, 2011, at 12:28 PM by 158.35.225.240 -
Changed line 40 from:

The mass and length of a pendulum can be determined by tracking the horizontal position of the pendulum (x). The following is a MATLAB script (pendulum.m) that runs the Index-3 DAE through a series of simulations. As additional data is collected, the model predictions are adjusted to match the observed measurements. The starting values for mass are 1 kg and a length of 1 m.

to:

The mass and length of a pendulum can be determined by tracking the horizontal position of the pendulum (x). The following is a MATLAB script (pendulum.m) that runs the Index-3 DAE through a series of simulations. As additional data is collected, the model predictions are adjusted to match the observed measurements. The starting values for mass are 1 kg and a length of 1 meter.

March 16, 2011, at 12:27 PM by 158.35.225.240 -
Changed lines 42-43 from:
to:
March 16, 2011, at 12:26 PM by 158.35.225.240 -
Added lines 39-44:

The mass and length of a pendulum can be determined by tracking the horizontal position of the pendulum (x). The following is a MATLAB script (pendulum.m) that runs the Index-3 DAE through a series of simulations. As additional data is collected, the model predictions are adjusted to match the observed measurements. The starting values for mass are 1 kg and a length of 1 m.

The technique for aligning measured and model values is termed Moving Horizon Estimation. This is a technique for parameter estimation with differential and algebraic equation models. In this case there is no steady state data available. The mass and length can be determined by observing the time series of horizontal positions.

May 26, 2010, at 06:06 AM by 158.35.225.240 -
Changed lines 37-38 from:
  • (:html:)<a href="http://apmonitor.ath.cx/online/plot.php?d=pendulum&f=SV(1).xml">Vertical Motion</a>(:htmlend:)
  • (:html:)<a href="http://apmonitor.ath.cx/online/plot.php?d=pendulum&f=SV(2).xml">Horizontal Motion</a>(:htmlend:)
to:
  • (:html:)<a href="/online/plot.php?d=pendulum&f=SV(1).xml">Vertical Motion</a>(:htmlend:)
  • (:html:)<a href="/online/plot.php?d=pendulum&f=SV(2).xml">Horizontal Motion</a>(:htmlend:)
March 06, 2010, at 02:45 AM by 206.180.155.75 -
Changed line 42 from:

(:html:)<font size=1><pre>

to:

(:html:)<font size=2><pre>

Changed lines 71-72 from:

(:htmlend:)

to:

(:htmlend:)

August 05, 2009, at 09:59 PM by 206.180.155.75 -
Changed line 7 from:

The following models are mathematically equivalent but are of different index order. The most natural form is an index-3 differential and algebraic (DAE) equation form, posed in terms of absolute position.

to:

The following models are mathematically equivalent but are of different index order. The most natural form is an index-3 differential and algebraic (DAE) equation form, posed in terms of absolute position. The index is the number of times the equations must be differentiated to achieve an ordinary differential equation (ODE) form.

June 25, 2009, at 03:15 PM by 158.35.225.227 -
Changed line 7 from:

The following models are mathematically equivalent but are of different order. The most natural form is an index-3 differential and algebraic (DAE) equation form, posed in terms of absolute position.

to:

The following models are mathematically equivalent but are of different index order. The most natural form is an index-3 differential and algebraic (DAE) equation form, posed in terms of absolute position.

June 25, 2009, at 01:26 PM by 158.35.225.227 -
Added lines 1-72:

Pendulum

The pendulum weight is located on the end of a massless cord suspended from a pivot, without friction. When given an initial push, it swings back and forth at a constant amplitude. Real pendulums are subject to friction and air drag, so the amplitude of the swing declines.

The following models are mathematically equivalent but are of different order. The most natural form is an index-3 differential and algebraic (DAE) equation form, posed in terms of absolute position.


Index-0 DAE (ODE) Model


Index-1 DAE Model


Index-2 DAE Model


Index-3 DAE Model


Predictions

  • (:html:)<a href="http://apmonitor.ath.cx/online/plot.php?d=pendulum&f=SV(1).xml">Vertical Motion</a>(:htmlend:)
  • (:html:)<a href="http://apmonitor.ath.cx/online/plot.php?d=pendulum&f=SV(2).xml">Horizontal Motion</a>(:htmlend:)

(:html:)<font size=1><pre>

APMonitor Modeling Language

http://www.apmonitor.com

Pendulum - Index 3 DAE

Model pend3

  Parameters
    m = 1
    g = 9.81
    s = 1
  End Parameters

  Variables
    x = 0
    y = -s
    v = 1
    w = 0
    lam = m*(1+s*g)/2*s^2
  End Variables

  Equations
    x^2 + y^2 = s^2
    $x = v
    $y = w
    m*$v = -2*x*lam
    m*$w = -m*g - 2*y*lam
  End Equations

End Model </pre></font> (:htmlend:)