Summary
Sigmoid functions contain a transition region between two constant values. As smoothed switches between quantities, these functions can be found in many fields of physics and engineering. The main motivation of the present work is the combined frictional effect between rigid bodies with the presence of different kinematic quantities. In several cases of modelling, it is not enough to consider a few parameters -- magnitude and steepness of the transition -- but the shape of the transition curve has to be known in more details. By choosing a special sigmoid function and applying appropriate transformations, a wide range of other sigmoid curves can be expanded by using either Fourier series or Legendre polynomials. It is demonstrated, that the resulting approximate models can be applied effectively for the qualitative analysis of dynamic problems of rigid bodies with coupled friction effect between slip and spin.
