## A compressible flow analogue in limit, cycle analysis and synthesis |

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actual equation(s Analytical Dynamics approached arbitrary function autonomous become infinite body force Brooklyn characteristic curve circular limit cycle closed trajectory constants Cornell University corresponding cycle configuration cycle(s Darboux denote density function determine differen Engineering Mechanics equa Equation 15 Equation 5a equation of motion equations 10a equations 9 equivalent system establish the validity exist explicit solution extended to include figure Ij Fluid Analogy fluid flow focus functional relationship given system implies Integral Invariants inverse problem Jacob!an Kinorsky Lagrangian form limit cycle-focus configuration necessary and sufficient non-autonomous system non-linear obtained Ordinary Differential Equations origin paper parameter particular solution particular system perfect gas phase plane phase portrait phase trajectory physical interpretation plane flow power series pressure-density relation representative point respectively satisfied scalar singular point solution surface space with coordinates stable limit cycle system of ordinary thesis three independent variables three-dimensional space tial equations unit circle unstable variable-separable vector equation velocity