# ex_caraxis: The Car Axis Mechanical Problem, Index 3 DAE In deTestSet: Test Set for Differential Equations

## Description

A rather simple multibody system, describing the behavior of a car axis on a bumpy road.

It is a differential algebraic equation of index 3

## Usage

 ```1 2 3``` ```caraxis (times = seq(0, 3, by = 0.01), yini = NULL, dyini = NULL, parms = list(), printmescd = TRUE, method = mebdfi, 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. `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. `method ` the solver to use; only `mebdfi` available for now `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 3 are printed `parms ` list of parameters that overrule the default parameter values `... ` additional arguments passed to the solver .

## Details

The default parameters are: eps = 1e-2, M = 10, L = 1, L0 = 0.5, r = 0.1, w = 10, g = 1

## 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 <[email protected]>

Francesca Mazzia <[email protected]>

## Examples

 ```1 2 3 4 5``` ```out <- caraxis() plot(out, lwd = 2, mfrow = c(3, 4)) # compare with reference solution out[nrow(out),2:11]-reference("caraxis") ```

deTestSet documentation built on May 29, 2017, 2:56 p.m.