Abstract
The paper suggests an explicit form of a general integral of motion for some classes of dynamical systems including n-degrees of freedom Euler–Lagrange systems subject to ( n - 1 ) virtual holonomic constraints. The knowledge of this integral allows to extend the classical results due to Lyapunov for detecting a presence of periodic solutions for a family of second order systems, and allows to solve the periodic motion planning task for underactuated Euler–Lagrange systems, when there is only one not directly actuated generalized coordinate. As an illustrative example, we have shown how to create a periodic oscillation of the pendulum for a cart–pendulum system and how then to make them orbitally exponentially stable following the machinery developed in [A. Shiriaev, J. Perram, C. Canudas-de-Wit, Constructive tool for an orbital stabilization of underactuated nonlinear systems: virtual constraint approach, IEEE Trans. Automat. Control 50 (8) (2005) 1164–1176]. The extension here also considers time-varying virtual constraints.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
