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Vol 71, No 3 (2016)
- Year: 2016
- Articles: 5
- URL: https://journals.rcsi.science/0027-1330/issue/view/10001
Article
Libration points of a rotating complexified triangle
Abstract
Similarities and differences between the force fields of a classical real dipole and a complex dipole are analyzed. The complex dipole is a pair of points equipped with complex conjugate masses and situated in a complex domain. The results of this analysis are used in the problem of motion of a material point in the field of attraction of a triangle uniformly rotating in its plane about its center of mass. It is assumed that a complex dipole is assigned to each vertex of the triangle. The existence and stability of libration points are studied. In particular, it is shown that there exist libration points outside the plane of the triangle.
51-57
Motion of a wheel on snow
Abstract
A model of a snow layer represented by a continuous set of columns whose deformations are described by the nonlinear model of an ideal elastoplastic continuous medium with viscous properties is proposed. Under the action of a rigid wheel on snow, the field of shear stresses is specified by the law of dry friction. Prom the equations of motion describing the plane-parallel motion of the wheel, there are determined a zone of contact of the wheel with snow, the steady motions of the wheel, and a mode of slipping the wheel. The numerical results are given in tables and figures. These results are obtained by solving the nonlinear equations of motion containing definite integrals with variable integration limits.
58-64
Brief Communications
Uniqueness of weak solutions to dynamic problems in the elasticity theory with boundary conditions of Winkler and inertial types
Abstract
A uniqueness theorem for the weak solution of an initial-boundary value problem in the anisotropic elasticity theory with the boundary conditions that “do not conserve” energy, namely, with the impedance and inertial type conditions is proved. The chosen method of proof does not require the positive definiteness of the elastic constant tensor (the case that may arise when solving the problems by the homogenization method for composite materials), but it requires to take the energy variation law as a postulate.
65-68
Exact solutions to an evolution equation of plastic layer flow on a plane
Abstract
The flow of a thin plastic layer between two rigid plates approaching each other in the normal direction is considered. The kinematics of plastic layer flow is studied. An evolution equation describing the free boundary of the flow region is derived. The similarity solutions to this equation are analyzed. It is shown that the evolution equation can be reduced to a particular case of the nonlinear heat conduction equation. New exact particular solutions to the evolution equation are obtained using the variable separation method and the method of self-similar transformations.
69-72
Hydrodynamic interaction between a flat surface and an evaporating drop in its own superheated vapor in the case of small Reynolds and Knudsen numbers
Abstract
An expression for the force of interaction between a flat surface and an evaporating drop moving along the normal to this surface is obtained in the approximation of the hydrodynamic lubrication theory. The gap between the surface and the drop is small. The effects of the slip, the temperature jump, and the evaporation rate of the drop on the time of variation of this gap are considered under the assumption that the temperature of the flat surface exceeds the boiling temperature of the drop.
73-76