Speedy Motions of a Body Immersed in an Infinitely Extended Medium |
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Authors: | Paolo Buttà Giorgio Ferrari and Carlo Marchioro |
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Institution: | 1.Dipartimento di Matematica,SAPIENZA Università di Roma,Rome,Italy;2.Dipartimento di Matematica per le Decisioni Economiche, Finanziarie ed Assicurative,SAPIENZA Università di Roma,Rome,Italy |
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Abstract: | We study the motion of a classical point body of mass M, moving under the action of a constant force of intensity E and immersed in a Vlasov fluid of free particles, interacting with the body via a bounded short range potential Ψ. We prove that if its initial velocity is large enough then the body escapes to infinity increasing its speed without any
bound (runaway effect). Moreover, the body asymptotically reaches a uniformly accelerated motion with acceleration E/M. We then discuss at a heuristic level the case in which Ψ(r) diverges at short distances like gr
−α
, g,α>0, by showing that the runaway effect still occurs if α<2. |
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