Temat: całki eliptyczne - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Boundary-integral model of permanent magnet of a tube segment as shape
Autorzy:: Pawluk, K.
Sulima, R.
Powiązania:: https://bibliotekanauki.pl/articles/140403.pdf
Data publikacji:: 2011
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: magnes trwały
metoda całkowo-brzegowa
całki eliptyczne
permanent magnets
boundary integral method
elliptic integrals
Opis:: The magnetic field due to a permanent magnet of a tube-side segment as shape and of radial-oriented magnetization is considered. Such a sheet modelling a single pole of the magnet is used to express the suitable contribution to magnetic quantities. A boundary-integral approach is applied that is based on a virtual scalar quantity attributed to the magnet pole. Such an approach leads to express analytically the scalar magnetic potential and the magnetic flux density by means of the elliptic integrals. Numerical examples of the computed fields are given. The general idea of the presented approach is mainly directed towards designing the magnetic field within the air gap of electric machines with permanent magnets as an excitation source. Other technical structures with permanent magnets may be a subject of this approach as well.
Źródło:: Archives of Electrical Engineering; 2011, 60, 4; 413-432
1427-4221
2300-2506
Pojawia się w:: Archives of Electrical Engineering
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Mechanics of infinitesimal gyroscopes on helicoid-catenoid deformation family of minimal surfaces
Autorzy:: Kovalchuk, Vasyl
Gołubowska, Barbara
Mladenov, Ivaïlo M.
Powiązania:: https://bibliotekanauki.pl/articles/2128134.pdf
Data publikacji:: 2021
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: action-angle analysis
mechanics of infinitesimal gyroscopes
geodesic equations of motion
geodetic equations of motion
helicoid-catenoid deformation family of minimal surfaces
elliptic integrals
elliptic functions
analiza kąta działania
mechanika nieskończenie małych żyroskopów
równanie ruchu geodezyjne
całki eliptyczne
funkcje eliptyczne
rodzina deformacji helikoidów minimalnych powierzchni
rodzina deformacji katenoidów minimalnych powierzchni
Opis:: In this paper we explore the mechanics of infinitesimal gyroscopes (test bodies with internal degrees of freedom) moving on an arbitrary member of the helicoid-catenoid family of minimal surfaces. As the configurational spaces within this family are far from being trivial manifolds, the problem of finding the geodesic and geodetic motions presents a real challenge. We have succeeded in finding the solutions to those motions in an explicit parametric form. It is shown that in both cases the solutions can be expressed through the elliptic integrals and elliptic functions, but in the geodetic case some appropriately chosen compatibility conditions for glueing together different branches of the solution are needed. Additionally, an action-angle analysis of the corresponding Hamilton-Jacobi equations is performed for external potentials that are well-suited to the geometry of the problem under consideration. As a result, five different sets of conditions between the three action variables and the total energy of the infinitesimal gyroscopes are obtained.
Źródło:: Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 2; e136727, 1--10
0239-7528
Pojawia się w:: Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Mechanics of infinitesimal gyroscopes on helicoid-catenoid deformation family of minimal surfaces
Autorzy:: Kovalchuk, Vasyl
Gołubowska, Barbara
Mladenov, Ivaïlo M.
Powiązania:: https://bibliotekanauki.pl/articles/2173588.pdf
Data publikacji:: 2021
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: action-angle analysis
mechanics of infinitesimal gyroscopes
geodesic equations of motion
geodetic equations of motion
helicoid-catenoid deformation family of minimal surfaces
elliptic integrals
elliptic functions
analiza kąta działania
mechanika nieskończenie małych żyroskopów
równanie ruchu geodezyjne
całki eliptyczne
funkcje eliptyczne
rodzina deformacji helikoidów minimalnych powierzchni
rodzina deformacji katenoidów minimalnych powierzchni
Opis:: In this paper we explore the mechanics of infinitesimal gyroscopes (test bodies with internal degrees of freedom) moving on an arbitrary member of the helicoid-catenoid family of minimal surfaces. As the configurational spaces within this family are far from being trivial manifolds, the problem of finding the geodesic and geodetic motions presents a real challenge. We have succeeded in finding the solutions to those motions in an explicit parametric form. It is shown that in both cases the solutions can be expressed through the elliptic integrals and elliptic functions, but in the geodetic case some appropriately chosen compatibility conditions for glueing together different branches of the solution are needed. Additionally, an action-angle analysis of the corresponding Hamilton-Jacobi equations is performed for external potentials that are well-suited to the geometry of the problem under consideration. As a result, five different sets of conditions between the three action variables and the total energy of the infinitesimal gyroscopes are obtained.
Źródło:: Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 2; art. no. e136727
0239-7528
Pojawia się w:: Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:: Biblioteka Nauki

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