deTestSet (version 1.0)

pleiades: Motion of Inextensible Elastic Beam, ODE

Description

The pleiades problem is a problem from celestial mechanics, describing the motion of seven stars in the plane of coordinates xi, yi and masses mi = i (i = 1, ... 7).

It is a set of nonstiff ordinary differential equations of dimension 28.

Usage

pleiades (times = seq(0, 3.0, by = 0.01), yini = NULL, method = lsoda, ...)

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.

times

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

method

the solver to use

...

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

There are no parameters

References

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

Examples

out <- pleiades()
par(mfrow = c(3,3))
for (i in 1:7) plot(out[,i+1], out[,i+8], type = "l", main = paste("body ",i),
     xlab = "x", ylab = "y")


plot(0, 0 , type = "n", main = "ALL",
     xlab = "x", ylab = "y", xlim = c(-3, 4), ylim = c(-4, 5))
for (i in 1:7) lines(out[,i+1], out[,i+8], col = i, lwd = 2)

# compare with reference solution
max(abs(out[nrow(out),-1]- reference("pleiades")))