Local minimality properties of circular motions in \(1/r^\alpha\) potentials and of the figure-eight solution of the 3-body problem
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Publication:2077124
DOI10.1007/s42985-022-00148-5OpenAlexW4206259368WikidataQ114216449 ScholiaQ114216449MaRDI QIDQ2077124
Publication date: 22 February 2022
Published in: SN Partial Differential Equations and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2201.01205
Nonlinear boundary value problems for ordinary differential equations (34B15) Periodic solutions to ordinary differential equations (34C25) (n)-body problems (70F10) Optimality conditions for problems involving ordinary differential equations (49K15)
Cites Work
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- On the minimizing properties of the 8-shaped solution of the 3-body problem
- Platonic polyhedra, topological constraints and periodic solutions of the classical \(N\)-body problem
- Hip-hop solutions of the \(2N\)-body problem
- Conjugate points in the calculus of variations and optimal control theory via the quadratic form theory
- Quadratic functionals with general bounday conditions
- On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem
- Braids with the symmetries of Platonic polyhedra in the Coulomb (N+1)-body problem
- Sufficient conditions for variational problems with variable endpoints: Coupled points
- Applications of time scale symplectic systems without normality
- Riccati equations for abnormal time scale quadratic functionals
- New Second-Order Optimality Conditions for Variational Problems with C2 -Hamiltonians
- Sufficiency and the Jacobi Condition in the Calculus of Variations
- Coupled Points in the Calculus of Variations and Applications to Periodic Problems
- Sufficiency Criteria via Focal Points and via Coupled Points
- A Minimizing Property of Keplerian Orbits
- Constrained Regular LQ-Control Problems
- The existence of simple choreographies for theN-body problem—a computer-assisted proof
- Braids in classical dynamics
- On the stability of periodic N-body motions with the symmetry of Platonic polyhedra
- Computer assisted proofs for nonsymmetric planar choreographies and for stability of the Eight
- Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems
- Minima of the action integral in the Newtonian problem of 4 bodies with equal masses: `Hip-hop' orbits
- A remarkable periodic solution of the three-body problem in the case of equal masses
