Integrability of generalized Jacobi problem

    2005, Volume 10, Number 4, pp.  437-461

    Author(s): Bardin B. S., Maciejewski A. J., Przybylska M.

    We consider a point moving in an ellipsoid $a_1x_1^2+a_2x_2^2+a_3x_3^2=1$ under the influence of a force with quadratic potential $V=\frac{1}{2}(b_1x_1^2+b_2x_2^2+b_3x_3^2)$. We prove that the equations of motion of the point are meromorphically integrable if and only if the condition $b_1(a_2-a_3)+b_2(a_3-a_1)+b_3(a_1-a_2)=0$ is fulfilled.
    Keywords: Jacobi problem, integrability, differential Galois group, monodromy group
    Citation: Bardin B. S., Maciejewski A. J., Przybylska M., Integrability of generalized Jacobi problem , Regular and Chaotic Dynamics, 2005, Volume 10, Number 4, pp. 437-461

    Download File
    PDF, 1.01 Mb