andrews | R Documentation |
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
andrews (times = seq(0, 0.03, by = 0.03/100), yini = NULL, dyini = NULL,
parms = list(), printmescd = TRUE, method = mebdfi,
atol = 1e-7, rtol = 1e-7, maxsteps = 1e+05, ...)
yini |
the initial (state) values for the DE system. If |
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 |
parms |
list of parameters that overrule the default parameter values |
printmescd |
if TRUE the mixed error significant digits computed using the reference solution at time 0.03 are printed |
method |
the solver to use |
maxsteps |
maximal number of steps per output interval taken by the solver |
... |
additional arguments passed to the solver . |
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)
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.
Karline Soetaert <karline.soetaert@nioz.nl>
Francesca Mazzia <mazzia@dm.uniba.it>
http://archimede.dm.uniba.it/~testset
out <- andrews()
plot(out, lwd = 2, which = 1:9)
refsol <- reference("andrews")
max(abs(out[nrow(out),-1] - refsol)/refsol)
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