New integrability conditions for differential constraints

• Published in: Systems & control letters Vol. 49; no. 5; pp. 335 - 345
• Main Authors: Tarn, Tzyh-Jong, Zhang, Mingjun, Serrani, Andrea
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.08.2003; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Differential forms; Exact sciences and technology; Holonomic constraints; Integrability conditions; Integrable systems; Integral equations; Mathematical analysis; Mathematics; Miscellaneous; Nonholonomic constraints; Ordinary differential equations; Sciences and techniques of general use; The Frobenius theorem; The Frobenius theorem; Differential forms; Nonholonomic constraints; Integrable systems; Integrability conditions; Holonomic constraints; Condition; Holonomic system; Differential form; Integrability; Integrable system; Non holonomic system; Dynamical system
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/S0167-6911(03)00112-9

This paper discusses differential-form-based integrability conditions for dynamic constraints using the Frobenius theorem. The conditions can be used for the classification of holonomic and nonholonomic constraints. Some of the previous conditions used for this purpose are only sufficient. The conditions presented here are both necessary and sufficient. The paper's main interest is on differential constraints for under-actuated mechanical systems. Different from many discussions in classical mechanics that deal with mostly on kinematics constraints, the constraints discussed here are from the Lagrange equations, which correspond to unactuated part of the system dynamics.