We present a new exact solution of the thermal diffusion equations for steady-state shear flows o... more We present a new exact solution of the thermal diffusion equations for steady-state shear flows of a binary fluid. Shear fluid flows are used in modeling and simulating large-scale currents of the world ocean, motions in thin layers of fluid, fluid flows in processes, and apparatuses of chemical technology. To describe the steady shear flows of an incompressible fluid, the system of Navier–Stokes equations in the Boussinesq approximation is redefined, so the construction of exact and numerical solutions to the equations of hydrodynamics is a very difficult and urgent task. A non-trivial exact solution is constructed in the Lin-Sidorov-Aristov class. For this class of exact solutions, the hydrodynamic fields (velocity field, pressure field, temperature field, and solute concentration field) were considered as linear forms in the x and y coordinates. The coefficients of linear forms depend on the third coordinate z. Thus, when considering a shear flow, the two-dimensional velocity fie...
In Sect. 10.1, we describe the coordinate systems used in the sequel. We present a phenomenologic... more In Sect. 10.1, we describe the coordinate systems used in the sequel. We present a phenomenological formula for the torque L due to the light pressure acting on a Sun satellite. The equations of the perturbed motion of the satellite in the presence of the force function are written. We note some results obtained in [1, 2] in the study of motion of a dynamically nonsymmetric or symmetric satellite relative to its center of mass under the action of the light pressure torque.
Rapid rotational motion of a dynamically asymmetric satellite relative to the center of mass is s... more Rapid rotational motion of a dynamically asymmetric satellite relative to the center of mass is studied. The satellite has a cavity filled with viscous fluid at low Reynolds numbers, and it moves under the action of gravitational torque and the external resistance torque. The rotational motions are considered within of the model of a quasi-rigid body whose center of mass moves in a circular orbit around the Earth. The problems of dynamics, generalized and complicated by accounting for various disturbing factor remain rather topical till now.
An analysis is presented of the rapid motion of a heavy rigid body about a fixed point in the pre... more An analysis is presented of the rapid motion of a heavy rigid body about a fixed point in the presence of outer drag, with the moment of drag forces assumed to be a linear function of the angular velocity. An analysis is presented of a system obtained after averaging with respect to Euler-Poinsot motion in the case of rapid rotations.
We present a new exact solution of the thermal diffusion equations for steady-state shear flows o... more We present a new exact solution of the thermal diffusion equations for steady-state shear flows of a binary fluid. Shear fluid flows are used in modeling and simulating large-scale currents of the world ocean, motions in thin layers of fluid, fluid flows in processes, and apparatuses of chemical technology. To describe the steady shear flows of an incompressible fluid, the system of Navier–Stokes equations in the Boussinesq approximation is redefined, so the construction of exact and numerical solutions to the equations of hydrodynamics is a very difficult and urgent task. A non-trivial exact solution is constructed in the Lin-Sidorov-Aristov class. For this class of exact solutions, the hydrodynamic fields (velocity field, pressure field, temperature field, and solute concentration field) were considered as linear forms in the x and y coordinates. The coefficients of linear forms depend on the third coordinate z. Thus, when considering a shear flow, the two-dimensional velocity fie...
In Sect. 10.1, we describe the coordinate systems used in the sequel. We present a phenomenologic... more In Sect. 10.1, we describe the coordinate systems used in the sequel. We present a phenomenological formula for the torque L due to the light pressure acting on a Sun satellite. The equations of the perturbed motion of the satellite in the presence of the force function are written. We note some results obtained in [1, 2] in the study of motion of a dynamically nonsymmetric or symmetric satellite relative to its center of mass under the action of the light pressure torque.
Rapid rotational motion of a dynamically asymmetric satellite relative to the center of mass is s... more Rapid rotational motion of a dynamically asymmetric satellite relative to the center of mass is studied. The satellite has a cavity filled with viscous fluid at low Reynolds numbers, and it moves under the action of gravitational torque and the external resistance torque. The rotational motions are considered within of the model of a quasi-rigid body whose center of mass moves in a circular orbit around the Earth. The problems of dynamics, generalized and complicated by accounting for various disturbing factor remain rather topical till now.
An analysis is presented of the rapid motion of a heavy rigid body about a fixed point in the pre... more An analysis is presented of the rapid motion of a heavy rigid body about a fixed point in the presence of outer drag, with the moment of drag forces assumed to be a linear function of the angular velocity. An analysis is presented of a system obtained after averaging with respect to Euler-Poinsot motion in the case of rapid rotations.
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Papers by Dmytro Leshchenko