Ultraspherical potential approximation in nonlinear symmetric free oscillations

✍ Scribed by Harry H. Denman

• Book ID: 104134223
• Publisher: Elsevier Science
• Year: 1968
• Tongue: English
• Weight: 436 KB
• Volume: 286
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(68)90582-6

✦ Synopsis

A new technique for approximating the period-amplitude relation for free symmetric nonlinear oscillations is presented. It involves the linearization, in ultraspherical polynomials, of a function derived from the potential. This technique is applied to systems with hardening and softening cubic nonlinearities, and the optimum ultraspherical parameter values

for small and large nonlinearities are determined. The results obtained for these cubits are compared with the exact solutions, and with those of other methods. The new results constitute a substantial improvement over previous ones.