Effects Of Non-conservative Forces Research Articles

The effect of nonconservative forces on the stability of systems with multiple frequencies and the Nicolai paradox

In our work, we formulate the problem on the instability of the conservative system with an arbitrary number of degrees of freedom with the addition of small nonconservative forces (positional and dissipa� tive). Instability can arise when the conservative sys� tem has a multiple frequency of vibrations. The insta� bility region was obtained in terms of matrices of per� turbations and eigenvectors corresponding to the double frequency. In the absence of the dissipation, this region is bounded by a conical surface. The obtained results are generalized to the case of the fre� quency of an arbitrary multiplicity. In particular, it is shown that the addition of arbitrarily small circulatory forces typically results in the destabilization of the sys� tem with a multiple frequency. Then alongside with nonconservative positional forces, we investigate the effect of small dissipative forces. It is shown that, in this case, the addition of an arbitrarily small dissipa� tion generally transforms the instability region from a

Orbital determination and dynamics of resonant extrasolar planetary systems

AbstractIn this communication we review some properties and applications of mean-motion resonances in extrasolar planetary systems, with particular emphasis on the 2/1 commensurability. A first part is devoted to the dynamical structure of the 2/1 resonance, including (but not restricted to) the so-called apsidal corotations. In a second part we discuss the orbital evolution of resonant systems under the effects of non-conservative forces. Special attention is given to the use of apsidal corotations as markers of largescale orbital decay, possibly due to disk-planet interactions in primordial times. Finally, we analyze the interplay between dynamical analysis and orbital fitting. Using the HD82943 planetary system as an example, we discuss: (i) up to what point present orbital fits allow us to distinguish between different resonant configurations, and (ii) in what ways may the dynamical structure of resonances be used as a complementary part of the orbital fitting process.

Effects of non-conservative forces and nonholonomic constraints on Noether symmetries of a Lagrange system

The effects of non-conservative forces and nonholonomic constraints on Noether symmetries and conserved quantities of a Lagrange system are studied. When non-conservative forces or nonholonomic constraints are inserted in a Lagrange system, the Noether symmetries and the conserved quantities of the system may vary. Some Noether symmetries disappear, some new Noether symmetries emerge, and under certain conditions, some Noether symmetries will still remain. The conditions under which the Noether symmetries and the conserved quantities of the system will remain are given, and two examples are given to illustrate the application of the results.

Effects of non-conservative forces and nonholonomic constraints on Lie symmetrie s of a Hamiltonian system

The effects of non-conservative forces and nonholonomic constraints on Lie symmetries and conserved quantities of a Hamiltonian system are studied. When non-conservative forces or nonholonomic constraints are inserted in the Hamiltonian system, we obtain the conditions under which Lie symmetries, structure equation and conserved quantities of the system will remain present. The famous Emden equation and Appell-Hamel model are taken as examples to illustrate the application of the results.

Effects of non-conservative forces on Lie symmetries and conserved quantities of a Lagrange system

Non-conservative forces are exerted on a Lagrange system. Their effects on Lie symmetries, structure equation and conserved quantities of the system are studied. It can be seen that some Lie symmetries disappear and some new Lie symmetries emerge. Under certain conditions, some Lie symmetries will still remain present.

The Effect of Nonconservative Forces on Resonance Lock: Stability and Instability

Resonance lock, when a nonconservative force is present, may have a stable or an unstable character. We investigate which kinds of force yield stability and which yield instability, for any exterior resonance. We develop an analytical model, through which a criterion for stability is established. This criterion is checked by numerical integrations of the complete equations of motion with a conveniently chosen fictitious nongravitational force. Real nonconservative forces that have been acting in the present and past Solar System are analyzed in view of the deduced criterion. This explains the more stable character of resonance locks with gas drag and also the unstable character of resonance locks with forces induced by solar radiation and solar wind.

Effect of nonconservative forces on the neutralization of sputtered and other desorbed ions.

We discuss the effect of nonconservative forces on ions near surfaces and apply it to recent experimental work of Yu on the sputtering of ${\mathrm{O}}^{\mathrm{\ensuremath{-}}}$ from Nb and Va. These data displayed a significant deviation from the usual exponential dependence of yield on 1/${v}_{\ensuremath{\perp}}$. This deviation which occurs at low velocities was partially explained by Lang using a model in which the sputtered ion interacts with a single surface atom via a Morse potential. Although his model suggests that the effective velocity of the ion is larger than that observed it does not explain the full deviation of the effective velocity, which goes through a minimum and then turns up as the observed velocity goes to zero. In our paper we show that just by including a nonconservative force in the Lang model the full deviation can be explained nicely.