AN ANALOG COMPUTER STUDY OF VAN DER POL'S EQUATION AND ITS RESPONSE TO WHITE GAUSSIAN NOISE.
Abstract
Van der Pol's equation has a nonlinearity in the first derivative term and characteristics of the equation vary with a constant in the nonlinear term. Results of a computer study of the homogeneous equation compare favorably with phase plane data and periods obtained by numerical methods. Computer analysis of responses to random excitation show that the rms decreases exponentially toward the rms of the unexcited system as the constant in the nonlinear term is increased for constant noise input. Frequencies of the excited response become more random as excitation spectral density is increased but the predominant frequency is the same as for the homogeneous equation. The work presented is the result of an analog computer study of the response of the well-known and widely studied nonlinear van der Pol equation to different power spectral intensities of random white gaussian noise inputs. The results are presented in the form of time history plots and graphs of the amplitude response of van der Pol's equation to different noise spectral intensities and different constant coefficients of the nonlinear term in the equation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1965
- Accession Number
- AD0625372
Entities
People
- Eugene O. Conley
Organizations
- Air Force Institute of Technology