Abstract
There exists an Ehresmann connection on the fibred constrained sub-manifold defined by Pfaffian differential constraints. It is proved that curvature of the connection is closely related to the d-σ commutation relation in the classical nonholonomic mechanics. It is also proved that conditions of complete integrability for Pfaffian systems in Frobenius sense are equivalent to the three requirements upon the conditional variations in the classical calculus of variations: (1) the variations belong to the constrained manifold, (2) variational operators commute with differential operators, (3) variations satisfy the Chetaev's conditions. Thus this theory verifies the conjecture or experience of researchers of mechanics on the integrability conditions in terms of variation calculus.
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.
