The essence of this approach is to replace the standard Eulerian density-like variables for cloud and precipitation fields with a probabilistic
Lagrangian approach that applies point particles to represent the formation, growth, and fallout of cloud droplets, raindrops, and ice particles.
The stability of the
Lagrangian points make them prime candidates for building up future space based resources.
The
Lagrangian force density F comprises two parts of tension-compression [F.sub.S] and bending [F.sub.b] forces, i.e.
In this paper, we propose an alternative approach for the map from the canonical
Lagrangian variables to the Eulerian variables.
Then in this case we use the
Lagrangian derivative; for this we build the transported [bar.u]([theta]) on [[OMEGA].sub.0].
(ii) The subring of A* (X) containing divisors, Chern classes and
Lagrangian constant cycle subvarieties injects into cohomology.
ABSTRACT: We reformulated the
Lagrangian density for single fluid by using Caputo's fractional derivative, then from the fractional Euler-Lagrangian equation we obtained the equations that described the motion of single fluid in fractional form.
On the other hand, the choice N(t) = 1 for the gauge field on the
Lagrangian formulation represents no difficulty; however, if we want to implement the Hamiltonian formulation of the theory and thus the quantum formulation, we have to keep the gauge arbitrary.
Similar to GPS, a high-precision satellite navigation constellation which consists of libration point satellites in the Earth-Moon system is introduced to provide navigation information for deep space probes, which can be called, accordingly, the
Lagrangian point satellite navigation system.