Search

Single Stage to Orbit vehicles is present in literature for decades. Proposals from various companies emerged, but never happened. The feasibility of a proposed design to achieve the orbit in one stage can easily be approached with a numerical procedure that relies on a robust optimizer. A numerical demonstrator is proposed, based on a trajectory propagator and Differential Evolution (DE) optimizer. The optimization problem consists in achieving circular orbit parameters: altitude, speed and flight path angle at the end of the burn, by modulating thrust that is a polyline and the initial flight path angle. Norm 2 of difference between effective parameters and target ones is minimized. Although the DE optimizer handles constraints according the superiority of feasibility method, there is no benefit in using this approach. After many attempts, the problem has been formulated by adding weighted squares of constraints to the optimization function which is more or less equivalent to a penalty approach. The study enabled robust formulation, a certain parameterization of thrust versus time and the size of population to achieve good convergence. [ABSTRACT FROM AUTHOR]

Computer algebra methods are used to investigate the equilibrium orientations of a system of two bodies connected by a spherical hinge that moves along a circular orbit under the action of gravitational torque in the plane of the orbit. An algebraic method based on the resultant approach is applied to reduce the satellite stationary motion system of algebraic equations to a single algebraic equation in one variable, which determines the equilibrium configurations of the two-body system in the orbital plane. Classification of domains with equal numbers of equilibrium solutions is carried out using algebraic methods for constructing discriminant hypersurfaces. Discriminant curves in the space of system parameters that determine boundaries of domains with a fixed number of equilibria for the two-body system are obtained symbolically. Using the proposed approach it is shown that the satellite-stabilizer system can have up to 24 equilibrium orientations in the plane of a circular orbit. Some simple cases of the problem were studied in detail. [ABSTRACT FROM AUTHOR]

The authors describe an algorithm that allows calculating the parameters of maneuvers performed on several turns by the low-thrust engine, which ensure the flight of the active spacecraft to the specified vicinity of the target space object. The movement takes place in the vicinity of a circular orbit. Linearized equations of motion are used in solving the problem. The influence of the non-centrality of the gravitational field and the atmosphere is not taken into account. The determination of maneuver parameters takes place in three stages. At the first and third stages, the parameters of the pulse transition and the transition performed by the low-thrust engine, are determined analytically. At the second stage, the distribution of maneuvering between turns, which provides a solution to the meeting problem, is carried out by iterating over one variable. This method of solving the problem provides simplicity and high reliability of determining the parameters of maneuvers, which allows it to be used on board the spacecraft. The paper investigates the dependence of the total characteristic speed of solving the meeting problem on the number of turns of the flight and the magnitude of the engine thrust.

Background: Mechanical circulatory support devices, such as left ventricular assist devices, have recently been used in patients with heart failure as destination therapy but the formation of thrombus in blood pumps remains a critical problem. In this study, we propose a mechanical antithrombogenic method by impeller excitation using a magnetically levitated (Maglev) centrifugal pump. Previous studies have shown that one‐directional excitation prevents thrombus; however, it is effective in only one direction. In this study, we aimed to obtain a better effect by vibrating it in a circular orbit to induce uniform changes in the shear‐rate field entirely around the impeller. Methods: The blood coagulation time was compared using porcine blood. (1) The flow rate was set to 1 L/min, and applied excitation was at a frequency of 280 Hz and amplitude of 3 μm. (2) Moreover, the effect was compared by varying the frequency, amplitude, and direction of the excitation. In this experiment, the flow rate was set to 0.3 L/min. Results: (1) The thrombus formation time was 77 min without excitation and 133 min with excitation, which was 1.7 times longer. (2) The results showed no difference between (280 Hz, 3 μm) and (50 Hz, 16 μm) circular orbital excitations, and no directional difference, with thrombus formation of 2.5 times longer under all conditions than that without excitation. Conclusion: In the case of simple reciprocating excitation, the time was approximately 1.2 times longer. This indicated that the circular orbital excitation is more effective. [ABSTRACT FROM AUTHOR]

Computer algebra methods are used to determine the equilibrium orientations of a system of two bodies connected by a spherical hinge that moves in a central Newtonian force field on a circular orbit under the action of gravitational torque. Primary attention is given to the study of equilibrium orientations of the two-body system in the plane of the circular orbit. By applying symbolic differentiation, differential equations of motion are derived in the form of Lagrange equations of the second kind. A method is proposed for transforming the system of trigonometric equations determining the equilibria into a system of algebraic equations, which in turn are reduced by calculating the resultant to a single algebraic equation of degree 12 in one unknown. The roots of the resulting algebraic equation determine the equilibrium orientations of the two-body system in the circular orbit plane. By applying symbolic factorization, the algebraic equation is decomposed into three polynomial factors, each specifying a certain class of equilibrium configurations. The domains with an identical number of equilibrium positions are classified using algebraic methods for constructing a discriminant hypersurface. The equations for the discriminant hypersurface determining the boundaries of domains with an identical number of equilibrium positions in the parameter space of the problem are obtained via symbolic computations of the determinant of the resultant matrix. By numerical analysis of the real roots of the resulting algebraic equations, the number of equilibrium positions of the two-body system is determined depending on the parameters. [ABSTRACT FROM AUTHOR]

Computer algebra methods were used to find the stationary motions of the system of two bodies connected by a spherical hinge, that moves along a circular orbit under the action of gravitational field. The resultant calculation approach was applied to reduce the stationary motion system of algebraic equations to a single algebraic equation in one variable that determines spatial equilibrium configurations of the two-body system. Classification of domains with equal numbers of equilibrium solutions was done using algebraic methods for constructing discriminant hypersurfaces. Bifurcation curves in the space of system parameters that determine boundaries of domains with a fixed number of equilibrium orientations of the two-body system were obtained symbolically. The number of equilibria was found by analyzing the real roots of the algebraic equations in the space of parameters of the problem. [ABSTRACT FROM AUTHOR]

The basis for ensuring a high level of reliability and safety in dynamic operations is a comprehensive experimental development of products in conditions as close to the real conditions of operation as possible with the use of mathematical and simulation modeling. The technical task of conducting dynamic operations in orbit is analyzed, which in turn boils down to two basic: bringing the initial state of the spacecraft grouping into a given area of space and performing maneuvers in a given area of space during the active life. These management tasks and terminal requirements are considered to be initial in relation to the stochastic and minimax approaches that are offered for use in the construction of working algorithms. The method of developing a software-modeling complex of the decisive task of developing the means of conducting dynamic operations of the spacecraft has been proposed. The application is illustrated by examples.

Computer algebra methods were used to find the roots of a nonlinear algebraic system that determines the equilibrium orientations for a system of two bodies, connected by a spherical hinge, that moves along a circular orbit under the action of gravitational torque. To determine the equilibrium orientations of two connected bodies the system of 12 algebraic equations was decomposed using algorithms for Gröbner basis construction. The number of equilibria was found by analyzing the real roots of the algebraic equations from the calculated Gröbner basis. Evolution of the conditions for equilibria existence in the dependence of the parameter of the problem was investigated. The effectiveness of the algorithms for Gröbner basis construction was analyzed depending on the number of parameters for the problem under consideration. [ABSTRACT FROM AUTHOR]

The dynamics of a satellite moving in a central Newtonian force field in a circular orbit under the influence of aerodynamic and active damping torques depending on projections of the satellite's angular velocity is studied. A method for determining all equilibrium positions (equilibrium orientations) of the satellite in the orbital coordinate system given the values of aerodynamic torque, damping coefficients, and the principal central moments of inertia is proposed. In the case when the axes of the coordinate system attached to the satellite coincide with the axes of the orbital coordinate system, necessary and sufficient conditions for the asymptotic stability of the corresponding zero equilibrium position are obtained using the Routh–Hurwitz criterion. The domains with satisfied asymptotic stability conditions for the zero equilibrium position are analyzed depending on various dimensionless parameters of the problem. The damping of spatial oscillations of the satellite is numerically studied for various values of aerodynamic torque and damping coefficients. [ABSTRACT FROM AUTHOR]

In the framework of the model of M.A. Lavrentiev, the effect of internal elastic and dissipative forces on the rotational motion of the planet in a central gravitational field in a circular orbit is studied. The averaged equations of the rotational motion of the planet are derived. The stability of plane rotations is investigated. The analysis of the evolution of rotational motion depending on the values of the parameters and the initial conditions is carried out. [ABSTRACT FROM AUTHOR]

Computer algebra and numerical methods were used to investigate the properties of a nonlinear algebraic system determining the equilibrium orientations of a system of two bodies connected by a spherical hinge that move in a circular orbit under the action of a gravitational torque. Primary attention was given to equilibrium orientations of the two-body system in the special cases when one of the principal axes of inertia of both the first and second body coincides with the normal to the orbital plane, the radius vector, or the tangent to the orbit. To determine the equilibrium orientations of the two-body system, the set of stationary algebraic equations of motion was decomposed into nine subsystems. The system of algebraic equations was solved by applying algorithms for constructing Gröbner bases. The equilibrium positions were determined by numerically analyzing the roots of the algebraic equations from the constructed Gröbner basis. [ABSTRACT FROM AUTHOR]

The Aschenbach effect, the increasing behavior of the angular velocity of a timelike circular orbit with its radius coordinate, is found to extensively exist in rapidly spinning black holes to a zero-angular-momentum observer. It also has potential observation in the high-frequency quasi-periodic oscillations of X-ray flux. However, observing such effect remains to be a challenge in static and spherically symmetric black hole backgrounds. In this paper, we mainly focus on such issue. Starting with the geodesics, we analytically study the underlying properties of the timelike circular orbits, and show the conditions under which the Aschenbach effect survives. It is shown that the presence of the static point orbits and stable photon spheres would be the indicator of the Aschenbach effect. We then apply it to three characteristic black holes exhibiting different features. The results state that this effect is absent for both the Schwarzschild and Reissner-Nordström black holes. While, for the dyonic black hole in quasi-topological electromagnetics, there indeed exists the Aschenbach effect. This provides a first example that such effect exists in a non-spinning black hole background. Moreover, it also uncovers an intriguing property for understanding the black holes in nonlinear electrodynamics. [ABSTRACT FROM AUTHOR]