873 research outputs found
Nonlinear analysis of spacecraft thermal models
We study the differential equations of lumped-parameter models of spacecraft
thermal control. Firstly, we consider a satellite model consisting of two
isothermal parts (nodes): an outer part that absorbs heat from the environment
as radiation of various types and radiates heat as a black-body, and an inner
part that just dissipates heat at a constant rate. The resulting system of two
nonlinear ordinary differential equations for the satellite's temperatures is
analyzed with various methods, which prove that the temperatures approach a
steady state if the heat input is constant, whereas they approach a limit cycle
if it varies periodically. Secondly, we generalize those methods to study a
many-node thermal model of a spacecraft: this model also has a stable steady
state under constant heat inputs that becomes a limit cycle if the inputs vary
periodically. Finally, we propose new numerical analyses of spacecraft thermal
models based on our results, to complement the analyses normally carried out
with commercial software packages.Comment: 29 pages, 4 figure
Resonantly driven wobbling kinks
The amplitude of oscillations of the freely wobbling kink in the
theory decays due to the emission of second-harmonic radiation. We study the
compensation of these radiation losses (as well as additional dissipative
losses) by the resonant driving of the kink. We consider both direct and
parametric driving at a range of resonance frequencies. In each case, we derive
the amplitude equations which describe the evolution of the amplitude of the
wobbling and the kink's velocity. These equations predict multistability and
hysteretic transitions in the wobbling amplitude for each driving frequency --
the conclusion verified by numerical simulations of the full partial
differential equation. We show that the strongest parametric resonance occurs
when the driving frequency equals the natural wobbling frequency and not double
that value. For direct driving, the strongest resonance is at half the natural
frequency, but there is also a weaker resonance when the driving frequency
equals the natural wobbling frequency itself. We show that this resonance is
accompanied by translational motion of the kink.Comment: 19 pages in a double-column format; 8 figure
Generalized Variational Oscillation Principles for Second-Order Differential Equations with Mixed-Nonlinearities
Using generalized variational principle and Riccati technique, new oscillation criteria are established for forced second-order differential equation with mixed nonlinearities, which improve and generalize some recent papers in the literature
Integral averaging technique for the interval oscillation criteria of certain second-order nonlinear differential equations
AbstractWe present new interval oscillation criteria related to integral averaging technique for certain classes of second-order nonlinear differential equations which are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line. They generalize and improve some known results. Examples are also given to illustrate the importance of our results
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