This is a code for simulating an uniformly magnetized filament under rotating magnetic field. For the filament, dynamic Euler-beam equation is solved
where s is the arclength, x is the position, \rho is the mass line density, T is the tension force along the filament axis, EI is the bending rigidity, and f is the force line density.
- Filament implementation is validated against the Euler-Bernoulli beam solution, and script is given in filament validation. We have implemented Euler-Forward and Runge-Kutta 4 time-steppers. Although the RK4 converged to the analytical solution at the steady-state, we could not determine a stable time-step for Euler-forward.
- Convergence study is done by changing the number of elements of a filament and error is compared against the Euler-Bernolli beam solution.
Magnetic filament simulation scripts can be found here. In this study we changed the magnetic field angular rotation speed.