Wszystkie pola: Lagrange equation - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod
Autorzy:: Wang, Peng
Feng, Hui-Rong
Lou, Zhi-Mei
Powiązania:: https://bibliotekanauki.pl/articles/1033429.pdf
Data publikacji:: 2017-02
Wydawca:: Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:: conformal invariance
Lie symmetry
conserved quantities
thin elastic rod
Lagrange equation
Opis:: Basing on the analytical mechanics methods, the Lagrangian equations of thin elastic rod is constructed. The definition of conformal invariance for the Lagrange mechanics of elastic rod is given. The criterions that conformal invariance of elastic rod is the Lie symmetry are obtained based on the Lie point transformation group. The structure equation and conserved quantity deduced from conformal invariance of elastic rod are constructed. Take twist rod as an example to illustrate the application of the results got in this paper.
Źródło:: Acta Physica Polonica A; 2017, 131, 2; 283-287
0587-4246
1898-794X
Pojawia się w:: Acta Physica Polonica A
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: The Motion of a Bead Sliding on a Wire in Fractional Sense
Autorzy:: Baleanu, D.
Jajarmi, A.
Asad, J.
Błaszczyk, T.
Powiązania:: https://bibliotekanauki.pl/articles/1032352.pdf
Data publikacji:: 2017-06
Wydawca:: Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:: motion of a bead on a wire
Euler-Lagrange equation
fractional derivative
Grünwald-Letnikov approximation
Opis:: In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form. We first introduce the classical Lagrangian from the system model under consideration and obtain the classical Euler-Lagrange equation of motion. As the second step, we generalize the classical Lagrangian to the fractional form and derive the fractional Euler-Lagrange equation in terms of the Caputo fractional derivatives. Finally, we provide numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on a discretization scheme using a Grünwald-Letnikov approximation for the fractional derivatives. Numerical simulations verify that the proposed approach is efficient and easy to implement.
Źródło:: Acta Physica Polonica A; 2017, 131, 6; 1561-1564
0587-4246
1898-794X
Pojawia się w:: Acta Physica Polonica A
Dostawca treści:: Biblioteka Nauki

Artykuł

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