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Том 71, № 4 (2016)
- Год: 2016
- Статей: 5
- URL: https://journals.rcsi.science/0027-1330/issue/view/10002
Article
Displacement of a viscous fluid from a Hele-Shaw cell with a sink
Аннотация
It is found that the radial geometry does not stabilize the evolution of instability in the displacement of a more viscous fluid by a less viscous fluid from a circular Hele-Shaw cell with a sink. A linear analysis shows the absolute instability of the radial displacement front. The appearance of isolated fingers is observed during numerical simulations.
77-81
Two-stage destruction of a meteoroid with a final burst
Аннотация
The entry of a space body with a super orbital velocity into the Earth’s atmosphere is considered. Large aerodynamic loads, the forces of inertia, and the thermal flows to the body lead to the surface mass loss and to a possible mechanical failure. From observations it is known that the flight of a space body often ends with a powerful final burst. One of the adequate approaches to the estimation of energy release at the final stage of the body’s destruction is proposed to confirm the possibility of observing the effect of “thermal explosion” of a meteoroid.
82-86
Unsteady axisymmetric deformation of an elastic space with a spherical cavity under the action of body forces
Аннотация
A homogeneous elastic isotropic space with a spherical cavity is considered. Unsteady axisymmetric body forces are exerted on this space. Disturbances are absent at the boundary of the cavity. Series expansions in Legendre polynomials and their derivatives as well as the Laplace time transform are used. The solution is represented in an integral form with kernels in the form of Green’s functions. The structure of these kernels is determined and their originals are found. Numerical results are discussed.
87-92
A qualitative analysis of the brachistochrone problem with dry friction and maximizing the horizontal range
Аннотация
The problem of maximizing the horizontal coordinate of a point moving in a vertical plane under the action of gravity and dry friction and the corresponding brachistochrone problem are considered. The optimal control problem is reduced to a boundary value problem for a system of two nonlinear differential equations. A qualitative analysis of the trajectories of this system is carried out, their typical features are found and illustrated by numerical solving of the boundary value problem. It is shown that the normal component of the support reaction should be positive when moving along the optimal curve. The optimality of the found extremals is discussed.
93-97
Reduction of the Mathieu equation to a nonlinear equation of the first order
Аннотация
A second order equation with periodic coefficients is considered. It is shown that its analysis can be reduced to the study of a nonlinear equation of the first order. The second approximation is obtained for the first resonance region of the Mathieu equation. This approximation describes the behavior of solutions inside this resonance region and near it.
98-101