ex_pleiades: Motion of Inextensible Elastic Beam, ODE

In deTestSet: Test Set for Differential Equations

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, 
          printmescd = TRUE, method = lsoda,
          atol = 1e-6, rtol = 1e-6, ...)

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
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,
printmescd	if TRUE the mixed error significant digits computed using the reference solution at time 1e13 are printed
...	additional arguments passed to the solver .

Details

There are no parameters

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.

Author(s)

Karline Soetaert <[e-mail]>

Francesca Mazzia

References

http://archimede.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")))

deTestSet documentation built on Dec. 10, 2023, 3:04 a.m.