We develop a method, based on Darboux’ and Liouville’s works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without making any assumption on these elements’ form. We apply it to three dynamical systems: Lotka–Volterra, Lorenz and Rikitake. I. HISTORICAL OVERVIEW. In, Roger Liouville and A. Tresse developed a method for deciding whether ...

Over the last years, the demand for high strength and low weight materials, such as fabric-reinforced plastics, has grown in the aeronautical industry. By decreasing the production cost with short production cycle times and increasing reproducibility by automation, fabric-reinforced plastics are becoming increasingly better economical competitors to other construction materials such as for exam...

The buckling torque may be much less than the yield torque in very thin rectangular tubes under torsion. In this paper, simple closed-form formulae are presented for buckling analysis of long hollow rectangular tubes under torsion. By the presented formulae, one can obtain the critical torque or the critical angle of twist of the tube in terms of its geometrical parameters and material constant...

We present an alternative method to ray tracing that is based on a phase space description of light propagation. Liouville’s equation geometrical optics describes the evolution basic luminance space. At optical interface, laws describe non-local boundary conditions for luminance. A discontinuous Galerkin employed solve dielectric total internal reflection concentrator.

Aiming at the geomorphological and geometrical features of basin, a recognition approach combined with landform classification discriminant analysis is presented. First, k-means algorithm applied to digital elevation model data. The basic types landforms elevation, slope, relief amplitude are clustered, regions plains, mountains, hills have been separated. Focusing on plain its neighboring regi...