The transient response of certain third-ordernon-linear systems

✍ Scribed by H.R. Srirangarajan; P. Srinivasan

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 434 KB
• Volume: 29
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(73)80136-1

✦ Synopsis

In this paper a method of solving certain third-order non-linear systems by using the method of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solutio.n obtained on digital computer.