1. Free vibration

1.1 Setting up equations

In most cases (cf. ), the final model obtained can be represented simply as the assembly of massless torsion springs whose stiffness K and connectivity are known. The ends of each spring are linked to undeformable disks of inertia whose moment of inertia I has been identified. The parameterization characterizes the position and angular velocity of each disk in the model. From the kinetic energy and force function expressions written in terms of independent velocity and displacement parameters, Lagrange's formalism is used to obtain the differential system representing free torsional vibrations.

To illustrate this point, let's consider an unbranched model made up of n disks (figure