Dynamics of elastic strands with rolling contact

• We derive the dynamical equations for two rods in rolling contact.
• We use Euler–Poincaré symmetry reduction theory coupled with non-holonomic constraints.
• We show that non-holonomic contact introduces highly complex dynamics.

We derive the equations of motion for rolling elastic strands in persistent rolling contact. The equations, presented first in an abstract form, are obtained by using the theory of Euler–Poincaré reduction by symmetries, appropriately modified to incorporate nonholonomic rolling conditions via the Lagrange–d’Alembert principle. We then show how to apply that theory to a particular case of elastic strands in rolling contact with naturally circular cross-section, when the deformation of the cross-section at contact is assumed to be negligible. We also derive a consistent geometric theory of rolling motion for discrete strands, or chains, in contact. The paper is concluded by showing highly non-trivial chaotic behavior even in the most simple configurations.