deTestSet (version 1.0)

andrews: Andrews Squeezing Mechanism, Index 3 DAE

Description

The andrews problem describes the motion of 7 rigid bodies connected by joints without friction

It is a non-stiff second order differential algebraic equation of index 3, consisting of 14 differential and 13 algebraic equations

Usage

andrews (times = seq(0, 0.03, by = 0.001), yini = NULL, 
         dyini = NULL, parms = list(), method = "mebdfi", 
         atol = 1e-7, rtol = 1e-7, maxsteps = 1e+05, ...)

Arguments

yini

the initial (state) values for the DE system. If y has a name attribute, the names will be used to label the output matrix.

dyini

the initial derivatives of the state variables of the DE system.

atol

absolute error tolerance, either a scalar or a vector, one value for each y.

rtol

relative error tolerance, either a scalar or a vector, one value for each y,

times

time sequence for which output is wanted; the first value of times must be the initial time.

parms

list of parameters that overrule the default parameter values

method

the solver to use

maxsteps

maximal number of steps per output interval taken by the solver

...

additional arguments passed to the solver .

Value

• A matrix of class deSolve with up to as many rows as elements in times and as many columns as elements in yini, plus an additional column (the first) for the time value.

  There will be one row for each element in times unless the solver returns with an unrecoverable error. If yini has a names attribute, it will be used to label the columns of the output value.

Details

The default parameters are: parameter <- c(m1 = .04325, m2 = .00365, m3 = .02373, m4 = .00706 , m5 = .07050, m6 = .00706, m7 = .05498 , xa = -.06934, ya = -.00227 , xb = -0.03635, yb = .03273 , xc = .014 , yc = .072, c0 = 4530 , i1 = 2.194e-6, i2 = 4.410e-7, i3 = 5.255e-6, i4 = 5.667e-7, i5 = 1.169e-5, i6 = 5.667e-7, i7 = 1.912e-5, d = 28e-3, da = 115e-4,e=2e-2, ea = 1421e-5, rr = 7e-3, ra = 92e-5, l0 = 7785e-5, ss = 35e-3, sa = 1874e-5, sb = 1043e-5, sc = 18e-3, sd = 2e-2, ta = 2308e-5, tb = 916e-5, u = 4e-2, ua = 1228e-5, ub = 449e-5, zf = 2e-2, zt = 4e-2,fa=1421e-5, mom = 33e-3)

References

http://www.dm.uniba.it/~testset

Examples

out <- andrews()
plot(out, lwd = 2, which = 1:9)

refsol <- reference("andrews")
max(abs(out[nrow(out),-1] - refsol)/refsol)