A TENSOR METHOD FOR 3-DIMENSIONAL GEOMETRIC PROBLEMS. APPLICATION TO A PROBLEM IN RAILWAY VEHICLE DYNAMICS

The model used in developing the method is a rigid body moving in such a way that at least one point in the body retains its position in space. This motion is described by a second-order tensor. Considerable effort is devoted to defining this tensor in such a way as to yield a method satisfactory both theoretically and in practical application. The method is applied to a problem concerned with the dynamics of railway vehicles. The forces that steer a wheelset so that it stays on the track are generated in the surfaces of contact between the wheels and the rails. The forces in the contact surface depend among other things on the shape of the surface, and the shape depends on the position of the surface. Thus it is essential to be able to compute the contact positions.