Dynamics of mechanical systems with nonlinear nonholonomic constraints - II Differential equations of motion

摘要

Depending on how the nonholonomic constraints have been introduced to the Lagrange-D'Alemberts's principle, there are several differential equations of motion in the mechanics of nonholonomic systems. In this work, the most general type of differential equations of motion (fundamental to all known forms of the equations of motion for nonholonomic as well as holonomic systems) is derived. Here, the equations represent the generalization of Poincare's equation [1]. In published works [2, 3, 4, 5, 6], these have already taken into account nonlinear nonholonomic constraints and linear relations between real velocities and kinematic parameters. A method of dedication of the most generalized form of the equations of motion will be shown. It is followed by the analysis of particular cases. Then, it will be shown how to get form the generalized form to Maggi, Appell, Voronec, Chaplygin, Volterra, Ferrers, and Boltzmann-Hamel's equations appearing in nonholonomic systems. Further, a system of material points of variable mass, where the equations of motion are derived for the most general case of reactive forces and in case of constraints depending on mass variables will be considered. All theoretical considerations are illustrated with the analysis of the relevant nonholonomic model. Depending on how the nonholonomic constraints have been introduced to the Lagrange-D'Alemberts's principle, there are several differential equations of motion in the mechanics of nonholonomic systems. In this work, the most general type of differential equations of motion (fundamental to all known forms of the equations of motion for nonholonomic as well as holonomic systems) is derived. Here, the equations represent the generalization of Poincaré's equation.