ODEnetwork

The ODEnetwork package provides a framework to construct networks of second order differential equations in an efficient way. A solution of each network is calculated analytically. You are able to stress a network by changing the states of each differential equation. In this case, the network is solved in a numerical way. The states can be plotted over time.

Installation instructions

You can install the current github version using the devtools package and the following command in R:

devtools::install_github("surmann/ODEnetwork")

Example 1

The first example shows the definition of a single harmonic oscillator with mass 1 and a damping constant of 0.5. A spring connects the mass to the ground. It has the spring constant 4 and a distance of 2 from the ground.

masses <- 1
dampers <- as.matrix(0.5)
springs <- as.matrix(4)
distances <- as.matrix(2)

odenet <- ODEnetwork(masses, dampers, springs, distances = distances)

odenet <- setState(odenet, 3, 0)

A solution is calculated and plotted by the following code:

odenet <- simuNetwork(odenet, seq(0, 10, by = 0.1))
plot(odenet)
plot(odenet, state = "1vs2")

Example 2

A second example shows two connected oscillators over a time of 40s:

masses <- c(1, 2)
dampers <- diag(c(0.02, 0.1))
dampers[1, 2] <- 0.1
springs <- diag(c(4, 1))
springs[1, 2] <- 2
distances <- matrix(c(0, 0, 1, 0), ncol = 2)

odenet <- ODEnetwork(masses, dampers, springs, distances = distances)

odenet <- setState(odenet, c(1, 1), c(0, 0))
odenet <- simuNetwork(odenet, seq(0, 40, by = 0.01))
calcResonances(odenet)
odenet$state
plot(odenet)
plot(odenet, state = "1")
plot(odenet, state = "2")
plot(odenet, state = "1vs2")

The method setEvents fixes the position of the first oscillator to given values between 10s and 15s. In this example we chose a linear connection between the three time points.

eventdata <- data.frame(var = c("x.1", "x.1", "x.1")
                        , time = c(10, 13, 15)
                        , value = c(0, 1, 1)
                        , stringsAsFactors = TRUE
)
odenet <- setEvents(odenet, eventdata, type = "linear")
odenet <- simuNetwork(odenet, seq(0, 40, by = 0.01))
plot(odenet)
plot(odenet, state = "1")
plot(odenet, state = "2")
plot(odenet, state = "1vs2")

Contact

Please use the issue tracker for any suggestions, bugs or hints.