A note on the ultraspherical polynomial approximation method of averaging
Abstract
The method of averaging based on ultraspherical polynomial approximation has been applied to several non-linear oscillation problems. In this paper it is shown that the above method can be interpreted as a Galerkin technique with an appropriate weight function. Even though the analysis is not rigorous enough mathematically, it does provide insight into this generalized method of averaging.
- Publication:
-
Journal of Sound Vibration
- Pub Date:
- July 1977
- DOI:
- 10.1016/0022-460X(77)90094-3
- Bibcode:
- 1977JSV....53...63R
- Keywords:
-
- Approximation;
- Average;
- Oscillations;
- Polynomials;
- Galerkin Method;
- Integral Equations;
- Nonlinear Equations;
- Vibration Damping;
- Weighting Functions;
- Physics (General)