0
2013
Impact Factor

# Borislav Gajic

 Dragovic V., Gajic B., Jovanović B. Note on Free Symmetric Rigid Body Motion 2015, vol. 20, no. 3, pp.  293-308 Abstract We consider the Euler equations of motion of a free symmetric rigid body around a fixed point, restricted to the invariant subspace given by the zero values of the corresponding linear Noether integrals. In the case of the $SO(n − 2)$-symmetry, we show that almost all trajectories are periodic and that the motion can be expressed in terms of elliptic functions. In the case of the $SO(n − 3)$-symmetry, we prove the solvability of the problem by using a recent Kozlov’s result on the Euler–Jacobi–Lie theorem. Keywords: Euler equations, Manakov integrals, spectral curve, reduced Poisson space Citation: Dragovic V., Gajic B., Jovanović B.,  Note on Free Symmetric Rigid Body Motion, Regular and Chaotic Dynamics, 2015, vol. 20, no. 3, pp. 293-308 DOI:10.1134/S1560354715030065
 Dragovic V., Gajic B. Four-Dimensional Generalization of the Grioli Precession 2014, vol. 19, no. 6, pp.  656-662 Abstract A particular solution of the four-dimensional Lagrange top on $e(4)$ representing a four-dimensional regular precession is constructed. Using it, a four-dimensional analogue of the Grioli nonvertical regular precession of an asymmetric heavy rigid body is constructed. Keywords: rigid body dynamics, Grioli precession, four-dimensional Lagrange case Citation: Dragovic V., Gajic B.,  Four-Dimensional Generalization of the Grioli Precession, Regular and Chaotic Dynamics, 2014, vol. 19, no. 6, pp. 656-662 DOI:10.1134/S1560354714060045
 Dragovic V., Gajic B. On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations 2012, vol. 17, no. 5, pp.  431-438 Abstract It is proven that the completely integrable general Kirchhoff case of the Kirchhoff equations for $B \ne 0$ is not an algebraic complete integrable system. Similar analytic behavior of the general solution of the Chaplygin case is detected. Four-dimensional analogues of the Kirchhoff and the Chaplygin cases are defined on $e(4)$ with the standard Lie–Poisson bracket. Keywords: Kirchhoff equations, Kirchhoff case, Chaplygin case, algebraic integrable systems Citation: Dragovic V., Gajic B.,  On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations, Regular and Chaotic Dynamics, 2012, vol. 17, no. 5, pp. 431-438 DOI:10.1134/S156035471205005X
 Dragovic V., Gajic B. Elliptic curves and a new construction of integrable systems 2009, vol. 14, no. 4-5, pp.  466-478 Abstract A class of elliptic curves with associated Lax matrices is considered. A family of dynamical systems on $e(3)$ parametrized by polynomial a with the above Lax matrices are constructed. Five cases from the family are selected by the condition of preserving the standard measure. Three of them are Hamiltonian. It is proved that two other cases are not Hamiltonian in the standard Poisson structure on $e(3)$. Integrability of all five cases is proven. Integration procedures are performed in all five cases. Separation of variables in Sklyanin sense is also given. A connection with Hess-Appel’rot system is established. A sort of separation of variables is suggested for the Hess-Appel’rot system. Keywords: elliptic curves, $L-A$ pair, integrability, Hess-Appel’rot system, separation of variables Citation: Dragovic V., Gajic B.,  Elliptic curves and a new construction of integrable systems, Regular and Chaotic Dynamics, 2009, vol. 14, no. 4-5, pp. 466-478 DOI:10.1134/S1560354709040042
 Dragovic V., Gajic B. Hirota–Kimura Type Discretization of the Classical Nonholonomic Suslov Problem 2008, vol. 13, no. 4, pp.  250-256 Abstract We constructed Hirota–Kimura type discretization of the classical nonholonomic Suslov problem of motion of rigid body fixed at a point. We found a first integral proving integrability. Also, we have shown that discrete trajectories asymptotically tend to a line of discrete analogies of so-called steady-state rotations. The last property completely corresponds to well-known property of the continuous Suslov case. The explicite formulae for solutions are given. In $n$-dimensional case we give discrete equations. Keywords: Hirota–Kimura type discretization, nonholonomic mechanics, Suslov problem, rigid body Citation: Dragovic V., Gajic B.,  Hirota–Kimura Type Discretization of the Classical Nonholonomic Suslov Problem, Regular and Chaotic Dynamics, 2008, vol. 13, no. 4, pp. 250-256 DOI:10.1134/S1560354708040023