Technically, this example demonstrates how to utilize a function as input argument to a function in a model.
From a modeling point of view, the example demonstrates in very
simplified way the basic approach to model distributed systems with
the Ritz method. The displacement field u(c,t) of a
particle (where c is the undeformed position and
t is time) is hereby approximated by space-dependent
mode shapes Φ(c) and time-dependent modal amplitudes
q(t), that is u = Φ(c)*q(t).
When inserting this decomposition in the equations of motion and
then integrating over all particles, terms such as ∫(Φ(c)
dc)*q(t) appear, where the time-invariant integral term can
be computed beforehand once with the Lobatto
method. By this approach the partial differential equations are
transformed to a system of ordinary differential equations.