A study of mechanical models in pursuit problems

In this work, we use elements of differential geometry, such as unit vectors, tangent and normal, and radius of curvature, to study the compatibility of mechanical models in two pursuit problems. In the first study concerning the problem of the tractrix curve, we show how the choice of a model of two particles connected by a rigid stem, at first a natural and intuitive choice, is incompatible with the other constraints of the problem. Soon after, we expand the discussion and consider the situation in which the two particles obey the kinematics of Pierre Bouguer’s pursuit problem. In this case, we show how the choice of an extensible hookean stem model connecting both particles is compatible with the other constraints of the problem. The free software Modellus is used to simulate the behavior of the forces necessary to justify the system’s kinematics. An interesting behavior of changes in the orientation of the acting forces over time is presented and discussed in light of the constraints to be respected and through the concept of relative velocity.

Keywords:
Pursuit curves; constraints; ICT’s