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Advances in Mathematical Physics
Volume 2017, Article ID 2580968, 12 pages
Research Article

Canonical Forms and Their Integrability for Systems of Three 2nd-Order ODEs

1Department of Mathematics, Azad Jammu and Kashmir University, Muzaffarabad, Pakistan
2Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

Correspondence should be addressed to Muhammad Ayub; moc.liamtoh@5buya_dammahum

Received 5 April 2017; Accepted 25 May 2017; Published 16 July 2017

Academic Editor: Mariano Torrisi

Copyright © 2017 S. Zahida et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Differential invariants and their corresponding canonical forms for systems of three 2nd-order ODEs possessing three-dimensional Lie algebras are constructed. Their extension up to th-order system of three 2nd-order ODEs is presented. Furthermore singularity in invariant structure for the canonical forms is investigated. In addition integrability of these canonical forms is discussed. Illustrative physical examples from mechanics of system of particles are provided.