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We treat the planar frictionless motion induced by a starting pulse on a two-body system with four degrees of freedom consisting of two equal rods hinged together. A full discussion of all possible planar forceless motions is given, and the hyperelliptic functions are found to be necessary. A particular case, namely the asymptotic one, in its two kinematic variants (open/closed) is faced. It is ruled...
In 1985 Franz Rothe [J. Reine Angew Math. 355 (1985) 129–138] found, by means of the thermodynamical equilibrium theory, an asymptotic estimate of the period of solutions of ordinary differential equations originated by predator–prey Volterra–Lotka model. We extend some of the Rothe's ideas to more general systems: $$\dot p\left( t \right) = - g\left( {q\left( t \right)} \right),\quad \dot q\left(...
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