Abstract
In engineering, as well as in physics, one often encounters implicit systems of ordinary differential equations of the form Fi(ẏ1…ẏm, y1…ym) = 0, i = 1,…, m, in the unknowns y1…ym, where the Jacobian matrix (∂Fi/∂ẏj)i,j is identically singular. We first state a condition under which the above equation may be solved. Then, we give a decomposition, which provides as a byproduct a clear-cut definition of the index. Since the Fi's must be differentiated an arbitrary number of times, we employ tools stemming from the differential geometry of infinite jets and prolongations like Lie-Bäcklund morphisms.
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.
