Series description of small oscillations in non-linear autonomous systems

✍ Scribed by John Beek

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 886 KB
• Volume: 32
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(77)80204-2

✦ Synopsis

Autohomous blvanate systems m w&h the non-hear terms are not rnultiphed by a small coefficient are mves@a&d Attention IS restncted to systems for which the real part of the charactenstic values of the locally hneanz4 system 18 small Expressmns for the vanation of the radius of the trajectory III the phase plane at a sven au&e, and for the vanation of the number of cycles with tune, are denved These expresslons take the form of truncated power serves m the radius. ~tb coeflklents gwen explicitly m terms of the derwatwes through the third order of the functions charactenzmg the system Both expressions are mtegrated The exponenti approach of a system to a lmut cycle IS worked out Numerical dlustratioas of the use of the expressions for the derwatives and for the approach to a-limit cycle are presented 1INTRowmoN