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We consider a task of software and mathematic defining the angular position (in roll and pitch) of a spacecraft during its orbital motion under the influence of gravity torque. We suggest a new algorithm of roll and pitch angles estimation by data of only angular rate sensor. One may apply the algorithm as an alternative to measurements of the infrared vertical sensor in case of its absence or failure. The algorithm is obtained based on a solution of the two-point boundary value problem by means of analytic synthesis of modal observer for discrete identification model. A reasonable choice of parameters of the identification model and estimation algorithm is presented. Mathematic simulation and statistic tests confirm the algorithm efficiency. The limits of the algorithm applicability by the values of angles and angular rates are determined. The limits of applicability of the suggested algorithm as well as its operating speed allow applying the algorithm in real time on board an orbiting spacecraft.

We show that a multihelical optical fiber at certain parameters can be used for the high efficient transformation of EH- and HE-modes to linearly polarized optical vortices with topological charge +|l| and –|l|, respectively. We establish that the even EH- and HE-modes are transformed to the x-polarized optical vortices, while the odd ones are converted to the y-polarized optical vortices. This effect allows one to control the linear polarization of the optical vortex by controlling the parity of the hybrid mode and vice versa.

The authors of the article set the following tasks: to reveal the origins of the idea of the “standard”, addressing the problems of “the highest degree of generality” and syncretistic fields of knowledge; to designate the semantic field of concepts “measurement” and “non-physical quantity” in the framework of clarification of the category “standard”; to consider the category of the standard in measuring physical quantities from the point of view of the concept’s evolution, its current status and scope of application; to designate the relevance of scientific interest in research of non-physical quantities; to problematize key ideas of the standard in the framework of the interdisciplinary approach.

This study deals with the problem of stabilizing spatial motion of a maneuverable aircraft with three controls and nine state parameters. In the task it is required to provide specified dynamic properties of the controlled plant at minimal control actions. For numeric matrices describing one of flight modes of a typical maneuverable aircraft the parameterized set of controllers by state vector is synthesized basing on the generalized Bass – Gura formula. This formula allows analytically calculating modal control for multi-input objects and simplifies parameterization of this control. The task of row-by-row minimization of gain matrix quadratic norm at fixed poles values is solved analytically by choosing the values of supplementary parameters which do not change the closed-loop control system spectrum. A technique for parameterization of two rows of three is proposed. In parameterized rows the minima are obtained at the condition of forced zeroing the coefficients corresponding to linear velocity. Based on simulation results the poles are chosen at which along with optimal supplementary parameters one may synthesize a controller allowing for specified range of initial conditions to obtain the most rapid transient with required dynamics and minimal control actions.

This paper deals with stabilizing spatial motion of a maneuverable aircraft with three controls and nine state parameters. It is required to provide specified dynamic properties of the controlled plant at minimal control actions.To solve the assigned task the modification of the Bass – Gura formula is suggested, which allows analytically synthesizing stabilizing modal control for multi-input objects and simplifies parameterization of this control.For numeric matrices describing one of flight modes of the typical maneuverable aircraft and for required dynamic properties of the closed-loop control system a parameterized analytic solution of the considering problem is obtained in the form of controller matrix. A control law providing small values of state vector components and of controls shifts is synthesized by choosing the parameters minimizing the sum of controller coefficients absolute values. The simulation results are shown.

In this paper we theoretically study the propagation of optical vortices (OVs) through a loop resonator (LR) on a multimode optical fiber. We demonstrate the presence in LRs of a resonance, which is in the inversion of the topological charge (TC) of the transmitted OV. We show that in the outcoming field the weights of the OVs with opposite TCs may be sensitive to wavelength variations of the LR’s length. Near the resonance points this property can be used for super-efficient control over the TC and orbital angular momentum of the outcoming field. We discuss application of this effect for temperature sensing. We also demonstrate the resonance power spikes in the loop and show that the resonance loop fields are the Hermite-Gaussian modes. In addition, we study the spectral characteristics of OV transmission and show feasibility of LR-based comb filters and delay lines for OVs.

We consider the light propagation in circular optical fibers with a higher-order flexural sound wave. The analytical expressions for fiber eigenstates and the corresponding propagation constant are obtained by applying the resonance perturbation theory to the wave equation and thoroughly analyzed. It is shown that the acosucto-optic interaction in the problem induces two travelling long-period helical fiber gratings characterized by a different order of rotational symmetry. In fact only one of them turns out to has a non-zero strength and gives rise to a resonance coupling of optical fiber modes with adjacent by 2 azimuthal numbers. A novel method of stable efficient wavelength tunable producing of optical vortices from a regular Gauss-like beam is demonstrated.

We solved the vector wave equation to obtain modes with azimuthal number 2 of weakly guiding twisted anisotropic optical fiber. We considered the mutual action of linear anisotropy of the fiber material, twisted mechanical stress, and spin-orbital interaction. We established that modes with azimuthal number 2 are represented by linearly or circularly polarized optical vortices depending on the interplay between anisotropy of the material and the twisting/ spin-orbit-interaction effect. We established analytical expressions for the corresponding propagation constants at arbitrary fiber parameters, such as a linear anisotropy, twisting, and spin-orbital-interaction. We demonstrated the orbital birefringence and optical Zeeman effect for high-order modes with azimuthal number 2 in twisted anisotropic fibers.

We demonstrate the ability to use multihelical and twisted anisotropic fibers to implement the all-fiber stable logical element controlled-controlled-NOT gate (Toffoli gate). In twisted anisotropic fibers, we imply the radial number and the topological charge of input optical vortex as the control bits and the circular polarization carries the target bit. In multihelical fiber, the circular polarization and the radial number carry the control bits, while the topological charge carries the target one.