Результаты поиска по 'polar system of coordinates':
Найдено статей: 3
  1. Rakcheeva T.A.
    Polypolar coordination and symmetries
    Computer Research and Modeling, 2010, v. 2, no. 4, pp. 329-341

    The polypolar system of coordinates is formed by a family of a parametrized on a radius isofocal of kf-lemniscates. As well as the classical polar system of coordinates, it characterizes a point of a plane by a polypolar radius ρ and polypolar angle φ. For anyone connectedness a family isometric of curve ρ = const – lemniscates and family gradient of curves φ = const – are mutually orthogonal conjugate coordinate families. The singularities of polypolar coordination, its symmetry, and also curvilinear symmetries on multifocal lemniscates are considered.

    Keywords: curves, focuses, multifocal lemniscates, Cassini ovals, polar system of coordinates, coordinate families, groups of symmetries, curvilinear symmetries.
    Views (last year): 1.
  2. Rakcheeva T.A.
    Polypolar lemniscate coordinate system
    Computer Research and Modeling, 2009, v. 1, no. 3, pp. 251-261

    The polypolar coordinate system, as well as classical polar, characterizes a point on a plane by polar radius ρ and polar angle φ, but utilizes multiple poles instead of one pole. Such referencing can be provided by a class of multifocal lemniscates. The family of isometric curves ρ=const — lemniscates — and family of gradient curves φ=const are mutually orthogonal conjugate families.

    Keywords: polypolar coordinate system.
    Citations: 3 (RSCI).
  3. Maksimenko M.V., Tikhonov A.A.
    Modification of the electrodynamic method for spacecraft attitude stabilization at circumpolar orbits
    Computer Research and Modeling, 2026, v. 18, no. 1, pp. 149-168

    For the three-axis stabilization of the spacecraft in the orbital coordinate system, including in the indirect equilibrium position, an electrodynamic control method is used based on the simultaneous use of two control torques that affect the dynamics of the spacecraft’s rotational motion in the Earth’s magnetic field (EMF), namely, the Lorentz torque and the torque of magnetic interaction. It is assumed that the spacecraft, equipped with an electric charge with a controlled vector of static moment of charge of the first order and a controlled intrinsic magnetic moment, moves in a Keplerian circular Earth orbit of arbitrary inclination. It was previously shown that combining two control systems, magnetic and Lorentz control, into a single electrodynamic control system (EDCS) makes it possible to successfully solve various problems of controlling the angular motion of spacecraft. Unlike many well-known studies performed for one or another approximate EMF model, this work does not impose restrictions on the accuracy of the EMF approximation. Previous studies have shown the limited capabilities of the EDCS for spacecraft moving in orbits close to the polar ones, due to the presence in this case of such points on the spacecraft trajectory in which it is possible for the lines of action of the geomagnetic induction vector and the spacecraft velocity vector relative to the EMF. Therefore, in this paper, the problem of overcoming these difficulties is posed and solved. A modification of the EDCS is proposed, based, firstly, on optimizing the control of the angular motion of the spacecraft and, secondly, on limiting the maximum value of the modulus of the vector of the center of charge relative to the center of mass of the spacecraft, which must be created during control. A method for selecting parameters for a modified EMF is recommended. The presented results of numerical experiments for spacecraft located in polar and circumpolar orbits not only demonstrate the operability of the proposed modification of the EDCS, but also indicate the possibility of technical implementation of the modified electrodynamic method of three-axis spacecraft stabilization.

    Keywords: spacecraft, Lorentz torque, magnetic torque, threeaxial stabilization, optimization, polar orbit.

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