Linear stability analysis of nonholonomic multibody systems

• Published in: International journal of mechanical sciences Vol. 198; p. 106392
• Main Authors: Agúndez, A.G., García-Vallejo, D., Freire, E.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.05.2021
• Subjects: Linearization; Multibody; Nonholonomic; Stability; Nonholonomic; Stability; Multibody; Linearization
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2021.106392

•Three procedures are illustrated to linearize the equations of nonholonomic systems.•Three nonholonomic systems are studied: a skateboard, a hoop and a torus.•The linear stability of these systems is analysed.•The values of the eigenvalues of the Jacobian matrices are discussed.•The characteristics of the linearization approaches are summarized. [Display omitted] This paper illustrates the application of three novel linearization procedures, recently validated with a well-acknowledged bicycle benchmark and valid for general multibody systems with holonomic and nonholonomic constraints, to study the linear stability of some examples of nonholonomic multibody systems. Despite the dynamics and control of mechanical systems with nonholonomic constraints have been widely researched and discussed, the linearization of their equations of motion and stability analyses along different types of trajectories are more uncharted subjects. In particular, the linear stability of the forward motion with constant velocity of three nonholonomic systems is analysed: a simplified skateboard model, similar to a Chaplygin sleigh; a hoop rolling without slipping, and a torus rolling without slipping. The nonlinear equations of motion of these systems are obtained by means of a multibody system dynamics approach. Three different procedures are used to perform the linearization of the equations of motion, leading to linear systems of different sizes. The values of the resulting eigenvalues are compared and discussed for each of the previously mentioned nonholonomic systems.