Kepler's problem in constant curvature spaces
From MaRDI portal
Publication:1202253
DOI10.1007/BF00049149zbMath0765.70007MaRDI QIDQ1202253
Alexander O. Harin, Valery V. Kozlov
Publication date: 25 February 1993
Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)
Related Items (69)
Regularization of the circular restricted three body problem on surfaces of constant curvature ⋮ Finiteness of polygonal relative equilibria for generalised quasi-homogeneous \(n\)-body problems and \(n\)-body problems in spaces of constant curvature ⋮ Stability and exact periodic solutions of indefinite equations arising from the Kepler problem on the sphere ⋮ Central configurations of the curved \(N\)-body problem ⋮ Universal chain structure of quadratic algebras for superintegrable systems with coalgebra symmetry ⋮ Coherent states for the Kepler-Coulomb problem on a sphere ⋮ Unnamed Item ⋮ Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2 ⋮ Unnamed Item ⋮ An integrable Hénon–Heiles system on the sphere and the hyperbolic plane ⋮ Rotopulsators of the curved \(N\)-body problem ⋮ Some integrable extensions of Jacobi's problem of geodesics on an ellipsoid ⋮ Eulerian relative equilibria of the curved 3-body problems in 𝐒² ⋮ Integrable systems on the sphere with elastic interaction potentials ⋮ All the Lagrangian relative equilibria of the curved 3-body problem have equal masses ⋮ The restricted three body problem on surfaces of constant curvature ⋮ \(N\)-body dynamics on an infinite cylinder: the topological signature in the dynamics ⋮ Integrability and Huygens' principle on symmetric spaces ⋮ The curved \(N\)-body problem: risks and rewards ⋮ Almost all 3-body relative equilibria on \(\mathbb{S}^2\) and \(\mathbb{H}^2\) are inclined ⋮ On the restricted \((N + 1)\)-body problem on surfaces of constant curvature ⋮ Existence of a lower bound for the distance between point masses of relative equilibria in spaces of constant curvature ⋮ Nonlinear Resonance in a Position-Dependent Mass-Duffing Oscillator System with Monostable Potentials Driven by an Amplitude-Modulated Signal ⋮ Collision trajectories and regularisation of two-body problem on \(S^2\) ⋮ Stability, periodic solution and KAM tori in the circular restricted \((N+1)\)-body problem on \({\mathbb{S}}^3\) and \({\mathbb{H}}^3\) ⋮ Dirac Particle in the Coulomb Field on the Background of Hyperbolic Lobachevsky Model ⋮ Lie and Noether point symmetries for a class of nonautonomous dynamical systems ⋮ Orbits in the problem of two fixed centers on the sphere ⋮ Classification of positive elliptic-elliptic rotopulsators on Clifford tori ⋮ Stability and bifurcation in the circular restricted \((N+2)\)-body problem in the sphere \(\mathbb{S}^2\) with logarithmic potential ⋮ On the stability of tetrahedral relative equilibria in the positively curved 4-body problem ⋮ Euler and mathematical methods in mechanics ⋮ Multiparticle systems. The algebra of integrals and integrable cases ⋮ Some remarks about the centre of mass of two particles in spaces of constant curvature ⋮ Unnamed Item ⋮ New integrable two-centre problem on sphere in Dirac magnetic field ⋮ Existence of a class of rotopulsators ⋮ Relations between integrable systems in plane and curved spaces ⋮ Position-Dependent Mass Systems: Classical and Quantum Pictures ⋮ The curved symmetric 2- and 3-center problem on constant negative surfaces ⋮ Reducing round-off errors in symmetric multistep methods ⋮ On the geometry of the phase spaces of some \(\text{SO}(2, 1)\) invariant systems ⋮ On the motion of a solid body on spherical surfaces ⋮ The geometric nature of Lie and Noether symmetries ⋮ Integrable problems of celestial mechanics in spaces of constant curvature ⋮ Bertrand systems on spaces of constant sectional curvature. The action-angle analysis ⋮ Relative equilibria of the restricted three-body problem in curved spaces ⋮ Variational property of periodic Kepler orbits in constant curvature spaces ⋮ Reduction and relative equilibria for the two-body problem on spaces of constant curvature ⋮ Stability of the polar equilibria in a restricted three-body problem on the sphere ⋮ Global symplectic regularization for some restricted 3-body problems on \(S^1\) ⋮ The spatial problem of 2 bodies on a sphere. Reduction and stochasticity ⋮ Relative equilibria in the 3-dimensional curved n-body problem ⋮ McGehee blow-up of the Kepler problem on surfaces of constant curvature ⋮ Dynamical systems. Transl. from the Russian ⋮ On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere ⋮ Some quantum mechanical problems in Lobachevsky space ⋮ An intrinsic approach in the curved \(n\)-body problem: the negative curvature case ⋮ Relative Equilibria in curved restricted 4-body problems ⋮ Quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces ⋮ An intrinsic approach in the curved $n$-body problem. The positive curvature case ⋮ Existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous n-body problems and the curved n-body problem ⋮ Gravitational and harmonic oscillator potentials on surfaces of revolution ⋮ Comment on “Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2” [J. Math. Phys. 46, 052702 (2005)] ⋮ Response to “Comment on ‘Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2’ ” [J. Math. Phys. 46, 052702 (2005)] ⋮ Figures of equilibrium of an inhomogeneous self-gravitating fluid ⋮ Integrable generalisations of Dirac magnetic monopole ⋮ Generalized problem of two and four Newtonian centers ⋮ Motion on the sphere: integrability and families of orbits
Cites Work
This page was built for publication: Kepler's problem in constant curvature spaces
