Implicit Numerical Integration for Periodic Solutions of Autonomous Nonlinear Systems

[+] Author and Article Information
G. A. Thurston

NASA Langley Research Center, Hampton, Va. 23655

J. Appl. Mech 49(4), 861-866 (Dec 01, 1982) (6 pages) doi:10.1115/1.3162628 History: Received February 01, 1982; Revised May 01, 1982; Online July 21, 2009


A change of variables that stabilizes numerical computations for periodic solutions of autonomous systems is derived. Computation of the period is decoupled from the rest of the problem for conservative systems of any order and for any second-order system. Numerical results are included for a second-order conservative system under a suddenly applied constant load. Near the critical load for the system, a small increment in load amplitude results in a large increase in amplitude of the response.

Copyright © 1982 by ASME
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