Determination of drillstring parameters and associated control

A method for modelling a drillstring in a wellbore, the method comprising providing a model of the drillstring, the model representing the drillstring by a sequence of alternating springs and elements, where each element describes the mass and/or the moment of inertia of a corresponding part of the drillstring and each spring represents at least one of: axial, torsional and/or bending stiffnesses of one of the corresponding parts of the drillstring, wherein the model describes one or more forces on each element by one or more systems of ordinary equations of first or second order, where each equation comprise a linear part that comprises constant coefficients and a non-linear part that includes one or more of: one or more non-linear terms, one or more non-smooth terms, one or more time dependent terms and/or one or more coupled terms; and the method comprises recalculating the model for a plurality of time steps, wherein recalculating the model for the respective time step comprises calculating one, two or three dimensional positions, orientations and/or associated derivatives of all of the elements for the respective time step based on one, two or three dimensional positions, orientations and/or associated derivatives of all element at a previous time step, by describing the non-linear part by a form of expansion with respect to time and solving the system of equations either analytically or by the use of exponential integrators for the duration of the respective time step. Also described is a method of cleaning a wellbore using the model from the above method.