# Created by Octave 3.2.4, Tue Nov 23 12:53:28 2010 EST <mockbuild@jetta.math.Princeton.EDU.private>
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newmark
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 -- Function File: X = newmark(M, C, K, F, DT, X0 = 0, X'0 = 0, ALPHA =
          1/2, BETA = 1/4, FLAGS = "")
     Computes the solution of second-order differential equations of
     the form

          M  X'' + C X' + K X = F

     where X' denotes the first time derivative of X.

     If the function is called without the assigning a return value
     then X is plotted versus time.

     *Inputs*

    M
          The mass of the body.

    C
          Viscous damping of the system.

    K
          Spring stiffness (restoring force coefficient).

    F
          The forcing function as a time sampled or impulse vector (see
          *Special Cases*).

    DT
          The time step - assumed to be constant

    X0
          Initial displacement, default is zero

    X'0
          Initial velocity, default is zero

    ALPHA
          Alpha Coefficient - Controls "artificial damping" of the
          system.  Unless you have a really good reason, this should be
          1/2 which is the default.

    BETA
          Beta Coefficient - This coefficient is used to estimate the
          form of the system acceleration between time steps.  Values
          between 1/4 and 1/6 are common. The default is 1/4 which is
          unconditionally stable.

    FLAGS
          A string value which defines special cases.  The cases are
          defined by unique characters as explained in *Special Cases*
          below.

     *Outputs*

    X
          Matrix of size (3, `length'(F)) with time series of
          displacement (X(1,:)), velocity (X(2,:)), and acceleration
          (X(3,:))

     *Special Cases*

     The FLAGS variable is used to define special cases of analysis as
     follows.

     "i"  - Impulse forcing function.  The forcing function, F is a
       vector of impulses instead of a sampled time history.  "n"  -
     The stiffness is non-linear.  In this case, K is a string
     which contains the name of a function defining the non-linear
      stiffness.



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Computes the solution of second-order differential equations of the form


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nlnewmark
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 -- Function File: X = nlnewmark(M, C, Q, F, DT, X0 = 0, X'0 = 0, ALPHA
          = 1/2, BETA = 1/4, FLAGS = "")
     Computes the solution of non-linear second-order differential
     equations of the form

          M  X'' + C X' + Q(X, X', X'')  = F

     where X' denotes the first time derivative of X and Q is a
     non-linear function.

     If the function is called without the assigning a return value
     then X is plotted versus time.

     *Inputs*

    M
          The mass of the body.

    C
          Viscous damping of the system.

    Q
          The name of a function that returns the value of the
          resisting force for a given displacement.  The form of Q must
          be:

               F = Q( X)

          where F is the restoring force for the state vector X = [U,
          U', U"]; displacement (U), velocity (U'), and acceleration.

    F
          The forcing function as a time sampled or impulse vector (see
          *Special Cases*).

    DT
          The time step - assumed to be constant

    X0
          Initial displacement, default is zero

    X'0
          Initial velocity, default is zero

    ALPHA
          Alpha Coefficient - Controls "artificial damping" of the
          system.  Unless you have a really good reason, this should be
          1/2 which is the default.

    BETA
          Beta Coefficient - This coefficient is used to estimate the
          form of the system acceleration between time steps.  Values
          between 1/4 and 1/6 are common. The default is 1/4 which is
          unconditionally stable.

    FLAGS
          A string value which defines special cases.  The cases are
          defined by unique characters as explained in *Special Cases*
          below.

     *Outputs*

    X
          Matrix of size (3, `length(F)') with time series of
          displacement (X(1,:)), velocity (X(2,:)), and acceleration
          (X(3,:))

     *Special Cases*

     The FLAGS variable is used to define special cases of analysis as
     follows.

     "i"  - Impulse forcing function.  The forcing function, F is a
       vector of impulses instead of a sampled time history.  "n"  -
     The stiffness is non-linear.  In this case, K is a string
     which contains the name of a function defining the non-linear
      stiffness.



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Computes the solution of non-linear second-order differential equations
of the f

