A numerical analysis of slow oscillations in dynamics of coupled systems

We study a system that models a problem in which an oscillatory unit is coupled to a passive medium. We analyze the case in which an RCL circuit is coupled to an RC circuit. Some numerical results indicate when slow oscillations occur in coupled systems

Solving Nonlinear Aeronautical Problems Using the Carleman Linearization Method

Many problems in aeronautics can be described in terms of nonlinear systems of equations. Carleman developed a technique to linearize such equations that could lead to analytical solutions of nonlinear problems. Nonlinear problems are difficult to solve in closed form and therefore the construction of such solutions is usually nontrivial. This thesis will apply the Carleman linearization technique to three model problems: a two-degree of-freedom (2DOF) ballistic trajectory, Blasius\u27 boundary layer, and Van der Pol\u27s equation and evaluate how well the technique can adequately approximate the solutions of these ordinary differential equations

On the stationary solutions of Van Der Pol's equation with a forcing term

Thesis (Ph.D.) Massachusetts Institute of Technology. Dept. of Mathematics, 1946.Vita.Bibliography: leaf 27.by Warren Simms Loud.Ph.D

On-line digital computer control of the NERVA nuclear rocket engine

The problem of on-line digital computer control of the NERVA nuclear rocket engine is considered. Proposed is a method of State Dependent State Variable Feedback (SDSVF) as a practical approach to the control of NERVA and other complex nonlinear and/or time-varying systems. The difficulties inherent in other design methods are avoided by defining the optimal closed loop system in terms of a desired transfer function, rather than a performance index to maximize or minimize

Multicorrelation analysis and state space reconstruction

Constructing a mathematical model of a nonlinear system involves developing methods for determining a set of nonlinear differential equations. Based on Floris Takens\u27 theory, the delayed-time space with a given time-series is created, where the first inflection of multicorrelation function is an approximation of the optimal delay time. The multicorrelation function is the generalization of the autocorrelation function into a higher dimension of the system. The standard Grassberger-Proccia algorithm computes the correlation dimension of an artificially generated data set, which involves measuring the distances between all pairs of points, and estimates the dimensionality of the nonlinear system. Finally, the governing differential equations are generated by using a polynomial least squares method. The generated state equations provide the possibility of predicting the system. The practical aspects of attractor reconstruction is discussed in this investigation, by using nonlinear ordinary differential equations with low degrees of freedom as examples

Non-Linear Oscillations of a Mixed Rayleigh-Van der Pol Type. Report no. 7701

No abstract available