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Wen'an Jiang, Lili Xia, Yanli Xu. Birkhoffian Formulations of Bessel Equation[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2019, 28(2): 234-237. doi: 10.15918/j.jbit1004-0579.17115
Citation: Wen'an Jiang, Lili Xia, Yanli Xu. Birkhoffian Formulations of Bessel Equation[J].JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2019, 28(2): 234-237.doi:10.15918/j.jbit1004-0579.17115
shu

Birkhoffian Formulations of Bessel Equation

doi:10.15918/j.jbit1004-0579.17115
  • 1.

    Department of Engineering Mechanics, Jiangsu University of Science and Technology, Zhenjiang 212003, China

  • 2.

    School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

  • 3.

    School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

  • Received Date:2017-07-30
    Abstract
  • The Birkhoffian mechanics is more general than the Hamilton mechanics, but only some dynamical systems can be realized as a Birkhoffian formulation. This paper proposes a novel Birkhoffian formulation for the classical Bessel equation. Based on the first method of Santilli, the Birkhoffian formulation of Bessel equation is established under the assumption that the Birkhoffian describes the total physical energy of the corresponding conservative systems. Zero and n-th order classical Bessel equations are studied to verify the effectiveness of the proposed formulation.
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    • References (25)
  • [1]
    Santilli R M. Foundations of theoretical mechanics Ⅱ[M].New York:Springer, 1983.
    [2]
    Broucke R. Equations of motion in phase space[J]. Hadronic J, 1979, 2(5):1122-1158.
    [3]
    Lumsden C J, Trainor L E H. On the statistical mechanics of constrained biophysical systems[J]. J Statistical Phys, 1979, 20(6):657-669.
    [4]
    Mei F X.On the Birkhoffian mechanics[J]. Int J Nonlinear Mech, 2001, 36(5):817-834.
    [5]
    Zheng G H,Chen X W, Mei F X. First integrals and reduction of the Birkhoffian system[J]. Journal of Beijing Institute of Technology, 2001, 10(1):17-22.
    [6]
    Liu S X, Liu C, Guo Y X. Geometric formulations and variational integrators of discrete autonomous Birkhoffian systems[J]. Chin Phys B, 2011, 20(3):034501.
    [7]
    Harding J, Romanowska A B. Varieties of Birkhoff systems part I[J]. Order,2017,34(1):45-68.
    [8]
    Harding J, Romanowska A B. Varieties of Birkhoff systems part Ⅱ[J]. Order,2017,34(1):69-89.
    [9]
    Junginger A, Main J, Wunner G. Construction of Darboux coordinates and Poincaré-Birkhoff normal forms in noncanonical Hamiltonian systems[J]. Physica D, 2017, 348:12-32.
    [10]
    Fu J L, Chen L Q.Perturbation of symmetries of rotational relativistic Birkhoffian systems and its inverse problems[J]. Phys Lett A, 2004, 324:95-103.
    [11]
    Mei F X, Wu H B.Birkhoff symmetry and Lagrange symmetry[J]. Journal of Beijing Institute of Technology, 2015, 24(1):1-3.
    [12]
    Zhang Y, Zhai X H. Noether symmetries and conserved quantities for fractional Birkhoffian systems[J]. Nonlinear Dyn, 2015, 81(1-2):469-480.
    [13]
    Zhang F, Li W, Zhang Y Y, et al. Conformal invariance and Mei conserved quantity for generalized Hamilton systems with additional terms[J]. Nonlinear Dyn,2016,84(4):1909-1913.
    [14]
    Boronenko T S. On the use of the autonomous Birkhoff equations in Lie series perturbation theory[J]. Celest Mech Dyn Astr, 2017, 127(2):139-161.
    [15]
    Chen X W, Mei F X.Singular points, closed orbit, stable manifolds and unstable manifolds of second order autonomous Birkhoff systems[J]. Journal of Beijing Institute of Technology, 1998, 7(4):330-336.
    [16]
    Chen X W, Mei F X. Existence ofperiodic solutions for higher order autonomous Birkhoff systems[J]. Journal of Beijing Institute of Technology, 2000, 9(2):125-130.
    [17]
    Mei F X. Stability for the manifold of equilibrium state of the autonomous Birkhoff system[J].Journal of Beijing Institute of Technology, 1997, 6(2):106-109.
    [18]
    Li Y M, Mei F X. Stability for manifolds of equilibrium states of generalized Birkhoff system[J]. Chin Phys B, 2010, 19(8):080302.
    [19]
    Jiang W A, Xia Z W, Xia L L. Approximation closure method for Birkhoffian system under random excitations[J]. Int J Dynam Control, 2016,6(1):1-8.
    [20]
    Guo Y X, Luo S K, Shang M, et al. Birkhoffian formulations of nonholonomic constrained systems[J]. Rep Math Phys, 2001, 47(3):313-322.
    [21]
    Das J, Everitt W N, Hinton D B, et al. The fourth-order Bessel-type differential equation[J]. Appl Anal,2004, 83(4):325-362.
    [22]
    Everitta W N, Kalfb H. The Bessel differential equation and the Hankel transform[J]. J Comput Appl Math, 2007, 208(1):3-19.
    [23]
    Parand K, Nikarya M. Application of Bessel functions for solving differential and integro-differential equations of the fractional order[J]. Appl Math Model,2014,38(15-16):4137-4147.
    [24]
    Yüzbaşı S. Improved Bessel collocation method for linear Volterraintegro-differential equations with piecewise intervals and application of a Volterra population model[J]. Appl Math Model, 2016, 40(9-10):5349-5363.
    [25]
    Cortés J C, Jódar L, Villafuerte L. Mean square solution of Bessel differential equation with uncertainties[J]. J Comput Appl Math, 2017, 309(C):383-395.
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