ex_crank: Slider Crank Mechanical Problem, Index 2 DAE

In deTestSet: Test Set for Differential Equations

Slider Crank Mechanical Problem, Index 2 DAE

Description

The crank problem is a constrained mechanical system including both rigid and elastic bodies

It is a differential algebraic equation of index 2, 24 equations.

Usage

crank (times=seq(0, 0.1, by = 0.001), yini = NULL, dyini = NULL, 
       parms = list(), printmescd = TRUE, method = mebdfi, 
       atol = 1e-6, rtol = 1e-6, maxsteps = 1e+06, 
       options = list(), ...) 

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.
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; only mebdfi available for now
maxsteps	maximal number of steps per output interval taken by the solver
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 0.1 are printed
options	a list which specifies the initial conditions used ini, whether the problem is stiff, and the damping. The default is list(ini=1,stiff=0,damp=0)
...	additional arguments passed to the solver .

Details

The default parameters are: M1 = 0.36, M2 = 0.151104, M3 = 0.075552, L1 = 0.15, L2 = 0.30, J1 = 0.002727, J2 = 0.0045339259, EE = 0.20e12, NUE = 0.30, BB = 0.0080, HH = 0.0080, RHO = 7870.0, GRAV = 0.0, OMEGA = 150.0

There are two default initial conditions - set with options(ini=x)

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 <[e-mail]>

References

url : archimede.dm.uniba.it/~testset

Simeon, B.: Modelling a flexible slider crank mechanism by a mixed system of DAEs and PDEs, Math. Modelling of Systems 2, 1-18 (1996);

Examples

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

# compare  with reference solution (only  the first seven components)
refsol <- reference("crank")
max(abs(out[nrow(out),2:8] - refsol[1:7])/refsol[1:7])     

deTestSet documentation built on July 9, 2023, 6:10 p.m.