Analytical solution of the damped Helmholtz-Duffing equation (Q714596)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Analytical solution of the damped Helmholtz-Duffing equation |
scientific article; zbMATH DE number 6092822
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analytical solution of the damped Helmholtz-Duffing equation |
scientific article; zbMATH DE number 6092822 |
Statements
Analytical solution of the damped Helmholtz-Duffing equation (English)
0 references
11 October 2012
0 references
Consider the differential equation \[ \ddot x+ Ax+ 2\nu\dot x+ Bx^2+\varepsilon x^3= 0.\tag{\(*\)} \] Under the assumption \(A= {3B^2+ 8\varepsilon\nu\over 9\varepsilon}\), the author derives an analytic solution of equation \((*)\) by using Jacobian elliptic functions.
0 references
mixed-parity nonlinear oscillator
0 references
quadratic nonlinearities
0 references
damped Helmholtz-Duffing oscillator
0 references
asymmetric behavior
0 references
0 references
