  We examine a variety of numerical methods that arise when considering
dynamical systems in the context of physics-based simulations of deformable
objects. Such problems arise in various applications, including animation,
robotics, control and fabrication. The goals and merits of suitable numerical
algorithms for these applications are different from those of typical numerical
analysis research in dynamical systems. Here the mathematical model is not
fixed a priori but must be adjusted as necessary to capture the desired
behaviour, with an emphasis on effectively producing lively animations of
objects with complex geometries. Results are often judged by how realistic they
appear to observers (by the "eye-norm") as well as by the efficacy of the
numerical procedures employed. And yet, we show that with an adjusted view
numerical analysis and applied mathematics can contribute significantly to the
development of appropriate methods and their analysis in a variety of areas
including finite element methods, stiff and highly oscillatory ODEs, model
reduction, and constrained optimization.
