Via Carlo Alberto 10, 10123 Torino, Italy
Department of Mathematics, University of Turin
The Non-holonomic Double Pendulum: an Example of Non-linear Non-holonomic System
2011, vol. 16, no. 5, pp. 417-442
An example of physically realizable non-linear non-holonomic mechanical system is proposed. The dynamical equations are written following a general method proposed in an earlier paper. In order to make this paper self-contained, an improved and shortened approach to the dynamics of non-holonomic systems is illustrated in preliminary sections.
A General Method for Writing the Dynamical Equations of Nonholonomic Systems with Ideal Constraints
2008, vol. 13, no. 4, pp. 283-315
The basic notions of the dynamics of nonholonomic systems are revisited in order to give a general and simple method for writing the dynamical equations for linear as well as nonlinear kinematical constraints. The method is based on the representation of the constraints by parametric equations, which are interpreted as dynamical equations, and leads to firstorder differential equations in normal form, involving the Lagrangian coordinates and auxiliary variables (the use of Lagrangian multipliers is avoided). Various examples are illustrated.