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Stationary states and moving planes

Gerhard Ströhmer (2008)

Banach Center Publications

Most of the paper deals with the application of the moving plane method to different questions concerning stationary accumulations of isentropic gases. The first part compares the concepts of stationarity arising from the points of view of dynamics and the calculus of variations. Then certain stationary solutions are shown to be unstable. Finally, using the moving plane method, a short proof of the existence of energy-minimizing gas balls is given.

Symmetries and currents in nonholonomic mechanics

Michal Čech, Jana Musilová (2014)

Communications in Mathematics

In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical theory...

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