Nonintegrability of the reduced planar three-body problem with generalized force

Three-body problems (70F07) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Non-integrability of the three-body problem
Integrability of Hamiltonian systems with homogeneous potentials of degrees \(\pm 2\). An application of higher order variational equations
Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
Partial integrability of Hamiltonian systems with homogeneous potential
On the meromorphic non-integrability of some \(N\)-body problems
Non-integrability of some Hamiltonians with rational potentials
Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
An algorithm for solving second order linear homogeneous differential equations
A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
Meromorphic parametric non-integrability; the inverse square potential
Galoisian obstructions to integrability of Hamiltonian systems. I.
Non-integrability criterium for normal variational equations around an integrable subsystem and an example: the Wilberforce spring-pendulum
The meromorphic non-integrability of the three-body problem
Curvature and geodesic instabilities in a geometrical approach to the planar three-body problem
Picard-Vessiot Extensions of Real Differential Fields
The three-body problem and equivariant Riemannian geometry
Differential Galois theory and non-integrability of Hamiltonian systems
Integrals in involution for groups of linear symplectic transformations and natural mechanical systems

This page was built for publication: Nonintegrability of the reduced planar three-body problem with generalized force