The R-x, R2-x Planes; Some New Ideas for the Study of Nonlinear Systems

Use of some new planes such as the R-x, R2-x (where R represents in the n-dimensional phase space, the radius vector from the origin to any point on the trajectory described by the system) is suggested for analysis of nonlinear systems of any kind. The stability conditions in these planes are given. For easy understanding of the method, the transformation from the phase plane to the R-x, R2-x planes is brought out for second-order systems. In general, while these planes serve as useful as the phase plane, they have proved to be simpler in determining quickly the general behavior of certain classes of second-order nonlinear systems. A chart and a simple formula are suggested to evaluate time easily from the R-x and R2-x trajectories, respectively. A means of solving higher-order nonlinear systems is also illustrated. Finally, a comparative study of the trajectories near singular points on the phase plane and on the new planes is made.

Ideas generated in conceptual design and their effects on creativity

Search of design spaces to generate solutions affects the design outcomes during conceptual design. This research aims to understand the different types of search that occurs during conceptual design and their effect on the design outcomes. Additionally, we study the effect of other factors, such as creativity, problem-solving style, and experience of designers, on the design outcomes. Two sets of design experiments, with experienced and novice designers, are used in this study. We find that designers employ twelve different types of searches during conceptual design for problem understanding, solution generation, and solution evaluation activities. Results also suggest that creativity is influenced positively by the type and amount of searches, duration of designing, and experience of designers.