A regularization of a system of differential equations of stellar dynamics
A regularization of a system of differential equations of stellar dynamics
V.P. Dolgachev
Paired collisions in the motion of stars (material points), moving in the three-dimensional space are regularized. It is assumed that a certain part of stars moves in a spherical homogeneous cloud (core) of a given density; another part of stars moves in a homogeneous concentric spherical layer (corona), surrounding the core and having a lower density. The remaining part of the stars moves in the free space. The KS transformation is applied for obtaining regular differential equations of motion, which are used in investigating the evolution of specific stellar systems.
Show AbstractFerroelectric domains and laser frequency doubling in Ba$_2$NaNb$_5$O$_{15}$ crystals
Ferroelectric domains and laser frequency doubling in Ba$_2$NaNb$_5$O$_{15}$ crystals
A.L. Alexandrovskii
The generation of the second harmonic of laser radiation in polydomain $Ba_{2}NaNb_{5}O_{15}$ crystals is investigated. Diffuse scattering of the second harmonic is observed in crystals with disordered domain structure, consisting of microdomains. It is concluded that the dimension of acicular microdomains in the direction of the polar axis of the crystal is about 10μm, whereas their transverse dimensions range from 1 to 3 μm. Crystals with periodic laminar domian structure (with a period of 12 μm) exhibit quasisynchronous, noncolinear second harmonic generation with angular width of generation peak of 22'. Such a process can be employed for laser frequency transformation. The second harmonic generation in polydomain barium-lithium and potassium-lithium niobates was also investigated. The results obtained for these materials are analogous to those for $Ba_{2}NaNb_{5}O_{15}$. The reasons for similarity of domain structures of the investigated crystals are discussed.
Show AbstractOn the symmetry of the restricted three-body problem
On the symmetry of the restricted three-body problem
L.G. Luкjanоv
The symmetry of solutions and the symmetry of the first integrals of the restricted three-body problem in Nechvile coordinates is examined. The equivalence between the symmetry of solutions and the symmetry of the first integrals is shown. The existence of two families of selfsymmetric solutions, each of which is a function of three arbitrary parameters is proven. An analogous study is performed for the rectilinear three-body problem.
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