scholarly journals Relative equilibria of dynamically symmetric CubeSat nanosatellite under the action of aerodynamic and gravitational torques

2019 ◽  
Vol 18 (2) ◽  
pp. 21-32
Author(s):  
E. V. Barinova ◽  
I. A. Timbai
Keyword(s):  
Circular Orbit ◽  
Aerodynamic Drag ◽  
Relative Equilibrium ◽  
Relative Equilibria ◽  
Mass Center ◽  
Atmospheric Density ◽  
Force Coefficient ◽  
Aerodynamic Moment ◽  
Gravitational Moment ◽  
Proper Rotation

Motion of a dynamically symmetric CubeSat nanosatellite around the mass center on the circular orbit under the action of aerodynamic and gravitational torques is considered. We determined the nanosatellite equilibrium positions in the flight path axis system. We took into account the fact that the CubeSat nanosatellite has a rectangular parallelepiped shape and, therefore, the aerodynamic drag force coefficient depends on the angles of attack and proper rotation. We obtained formulae which allow calculating the values of the angles of attack, precession and proper rotation that correspond to the equilibrium positions, depending on the mass-inertia and geometric parameters of the nanosatellite, the orbit altitude, and the atmospheric density. It is shown that if the gravitational moment predominates over the aerodynamic one, there are 16 equilibrium positions, if the aerodynamic moment predominates over the gravitational one, there are 8 equilibrium positions, and in the case when both moments have comparable values there are 8, 12 or 16 equilibrium positions. Using the formulae obtained, we determined the equilibrium positions of the SamSat-QB50 nanosatellite. We calculated the ranges of altitudes where SamSat-QB50 nanosatellite has 8, 12, or 16 relative equilibrium positions.

Numerical Calculation of the Force Coefficient for Cylindrical Shape Smokestack Covered with Corrugated Iron

2016 ◽  
Vol 821 ◽  
pp. 79-84
Author(s):  
Vladimira Michalcova ◽  
Lenka Lausova
Keyword(s):  
Numerical Calculation ◽  
Circular Cylinder ◽  
Numerical Modelling ◽  
Aerodynamic Drag ◽  
Cylindrical Shape ◽  
Force Coefficient ◽  
Ansys Fluent ◽  
Aerodynamic Drag Coefficient ◽  
Aerodynamic Roughness ◽  
Des Model

The article deals with the influence of a shape of the smokestacks casing on the final load from wind effects. It describes possibilities of defining an equivalent aerodynamic roughness and aerodynamic drag coefficient for numerical modelling of the flow around a circular cylinder. The aim is to determine the force coefficient for a smokestack of a cylindrical shape, which is sheeted with corrugated sheet metal. The flow around a smokestack is solved in software Ansys Fluent using the DES model.

An Analysis of the Efficiency of Electric Propulsion Engines for Maintaining a Low Orbit of Small Spacecraft

2020 ◽  
pp. 65-74
Author(s):  
V.V. Volotsuev ◽  
V.V. Salmin
Keyword(s):  
Electric Propulsion ◽  
Aerodynamic Drag ◽  
Specific Impulse ◽  
Active Movement ◽  
Engine Fuel ◽  
Low Thrust ◽  
Atmospheric Density ◽  
Small Spacecraft ◽  
Drag Forces ◽  
Electric Engine

This paper examines the problem of maintaining the plane parameters of the working orbit of a small spacecraft using an electric propulsion engine. In low working orbits, due to the Earth’s atmosphere, a spacecraft is subjected to aerodynamic drag forces, which results in a decrease in the radius of the orbit and a potential termination of the useful target functioning. The time parameters of the cyclogram for maintaining the working orbit of a small spacecraft with an electric low thrust engine are analyzed taking into account the variability of the atmospheric density. The cyclogram consists of sections of the passive and active movement under the action of the low thrust engine. For the satellite under study, suitable thrust parameters of the electric engine are selected, which allow the correction of the plane parameters of the low orbit. Using the characteristics of the thrust and specific impulse of the electric jet engine, fuel reserves for correction over a long period of time are calculated. The results of the analysis confirm the effectiveness of the electric propulsion engine in terms of fuel consumption for correction.

scholarly journals Bifurcations of relative equilibria in the 4- and 5-body problem

1988 ◽  
Vol 8 (8) ◽  
pp. 215-225 ◽  
Keyword(s):  
Equilateral Triangle ◽  
Body Problem ◽  
Relative Equilibrium ◽  
Isosceles Triangle ◽  
Relative Equilibria ◽  
Arbitrary Mass

AbstractThe equilateral triangle family of relative equilibria of the 4-body problem consists of three particles of mass 1 at the vertices of an equilateral triangle and the fourth particle of arbitrary mass m at the centroid. For one value of the mass m this relative equilibrium is degenerate. We show that families of isosceles triangle relative equilibria bifurcate from the equilateral triangle family as m passes through the degenerate value.The square family of relative equilibria of the 5-body problem consists of four particles of mass 1 at the vertices of a square and the fifth particle of arbitrary mass m at the centroid. For one value of the mass m this relative equilibrium is degenerate. We show that families of kite and isosceles trapezoidal relative equilibria bifurcate from the square family as m passes through the degenerate value.

Euler-type Relative Equilibria and their Stability in Spaces of Constant Curvature

2018 ◽  
Vol 70 (2) ◽  
pp. 426-450 ◽  
Author(s):  
Ernesto Pérez-Chavela ◽  
Juan Manuel Sánchez-Cerritos
Keyword(s):  
Constant Curvature ◽  
Algebraic Curve ◽  
Positive Measure ◽  
Relative Equilibrium ◽  
Relative Equilibria ◽  
Spectral Stability ◽  
Spaces Of Constant Curvature ◽  
Central Mass ◽  
Elliptic Case ◽  
The Masses

AbstractWe consider three point positivemasses moving onS2andH2. An Eulerian-relative equilibrium is a relative equilibrium where the three masses are on the same geodesic. In this paper we analyze the spectral stability of these kind of orbits where the mass at the middle is arbitrary and the masses at the ends are equal and located at the same distance from the central mass. For the case of S2, we found a positive measure set in the set of parameters where the relative equilibria are spectrally stable, and we give a complete classiûcation of the spectral stability of these solutions, in the sense that, except on an algebraic curve in the space of parameters, we can determine if the corresponding relative equilibriumis spectrally stable or unstable. OnH2, in the elliptic case, we prove that generically all Eulerian-relative equilibria are unstable; in the particular degenerate case when the two equal masses are negligible, we get that the corresponding solutions are spectrally stable. For the hyperbolic case we consider the system where the mass in the middle is negligible; in this case the Eulerian-relative equilibria are unstable.

scholarly journals Collective behaviour of large number of vortices in the plane

2013 ◽  
Vol 469 (2156) ◽  
pp. 20130085 ◽  
Author(s):  
Yuxin Chen ◽  
Theodore Kolokolnikov ◽  
Daniel Zhirov
Keyword(s):  
Vortex Dynamics ◽  
Initial Conditions ◽  
Relative Equilibrium ◽  
Relative Equilibria ◽  
Point Vortices ◽  
Collective Behaviour ◽  
Aggregation Model ◽  
Equal Strength ◽  
Artificial Damping ◽  
Analytical Formulae

We investigate the dynamics of N point vortices in the plane, in the limit of large N . We consider relative equilibria , which are rigidly rotating lattice-like configurations of vortices. These configurations were observed in several recent experiments. We show that these solutions and their stability are fully characterized via a related aggregation model which was recently investigated in the context of biological swarms. By using this connection, we give explicit analytical formulae for many of the configurations that have been observed experimentally. These include configurations of vortices of equal strength; the N +1 configurations of N vortices of equal strength and one vortex of much higher strength; and more generally, N + K configurations. We also give examples of configurations that have not been studied experimentally, including N +2 configurations, where N vortices aggregate inside an ellipse. Finally, we introduce an artificial ‘damping’ to the vortex dynamics, in an attempt to explain the phenomenon of crystallization that is often observed in real experiments. The diffusion breaks the conservative structure of vortex dynamics, so that any initial conditions converge to the lattice-like relative equilibrium.

scholarly journals Nonlinear stability of rotating pseudo-rigid bodies

1990 ◽  
Vol 427 (1873) ◽  
pp. 281-319 ◽  
Keyword(s):  
Nonlinear Stability ◽  
Relative Equilibrium ◽  
Relative Equilibria ◽  
Rigid Bodies ◽  
Stability Conditions ◽  
Second Variation ◽  
Nonlinear Stability Analysis ◽  
Elastic Bodies ◽  
The Stability ◽  
The Second Variation

A rigorous nonlinear stability analysis of rotating homogeneous elastic bodies is presented, which exploits the hamiltonian structure and symmetries inherent to homogeneous elasticity by means of the energy-momentum method. It is shown that stability of a relative equilibrium is implied by the definiteness of the second variation of a modified hamiltonian restricted to an appropriate subspace. The analysis makes crucial use of a special parametrization of the constrained space of admissible variations, which results in a nearly diagonal second variation. The stability conditions obtained by this method include the conditions for stability of the equilibrium configuration as a rigid body and satisfaction of the Baker-Ericksen inequalities. As an application of our results, we obtain complete, explicit stability conditions for a particular form of relative equilibria for three classes of materials: for two of these, Ciarlet-Geymonat and St Venant-Kirchhoff materials, these equilibria are always stable; for the third, a compressible Mooney-Rivlin material, both stable and unstable equilibria exist.

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