Motion equations of nonholonomic systems

What is it about?

A system is holonomic if its Lagrange function (only for the conservative elements) fulfils the Lagrange-d'Alembert equation (power balance equation). The holonomicity of the system enables the formulation of motion equations on the basis of Lagrange function, using Euler-Lagrange equations. Such a problem is considered for a simple electromechanical device. At first, equations of motion were formulated, just like for the holonomic system. It was checked that the power balance of the device was not fulfilled. This means that the system is nonholonomic. Parameters of elements and motion equations were identified. On the basis of literature a method of correction of nonholonomicity of the system by introducing additional virtual force into motion equations has been formulated. The result is equations that meet the power balance. On this basis, a method of determining motion equations for nonholonomic systems was proposed.

Featured Image

Why is it important?

We propose formulation a proper motion equations of electromechanical systems.

Perspectives