Angular Momentum and Topological Dependence of Kepler's Third Law in the Broucke-Hadjidemetriou-Hénon Family of Periodic Three-Body Orbits.

We use 57 recently found topological satellites of Broucke-Hadjidemetriou-Hénon's periodic orbits with values of the topological exponent k ranging from k=3 to k=58 to plot the angular momentum L as a function of the period T, with both L and T rescaled to energy E=-0.5. Upon plotting L(T/k) we find that all our solutions fall on a curve that is virtually indiscernible by the naked eye from the L(T) curve for nonsatellite solutions.

Gravitational waves from periodic three-body systems.

Three bodies moving in a periodic orbit under the influence of Newtonian gravity ought to emit gravitational waves. We have calculated the gravitational radiation quadrupolar waveforms and the corresponding luminosities for the 13+11 recently discovered three-body periodic orbits in Newtonian gravity. These waves clearly allow one to distinguish between their sources: all 13+11 orbits have different waveforms and their luminosities (evaluated at the same orbit energy and body mass) vary by up to 13 orders of magnitude in the mean, and up to 20 orders of magnitude for the peak values.

Three classes of newtonian three-body planar periodic orbits.

We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body orbits into families, which fall into four classes, with all three previously known families belonging to one class. The classes are defined by the orbits' geometric and algebraic symmetries.

Approximate action-angle variables for the figure-eight and periodic three-body orbits.

We use the maximally permutation-symmetric set of three-body coordinates that consist of the "hyper-radius" R=√[ρ(2)+λ(2)], the "rescaled area of the triangle" √[3]/2R(2) |ρ×λ|), and the (braiding) hyperangle Φ=arctan(2ρ·λ/λ(2)-ρ(2)) to analyze the "figure-eight" choreographic three-body motion discovered by Moore [Phys. Rev. Lett.

piN and pipiN couplings of the Delta(1232) and its chiral partners.

We investigate the interactions and chiral properties of the four spin-3/2 baryons N(-)(D13), N+(P13), Delta+(P33), and Delta(-)(D33) together with the nucleon. We construct the SU(2)R x SU(2)L invariant interactions between the spin-1/2 and spin-3/2 baryons with the aid of a new, specially developed spin and isospin projection technique for these baryon fields, where the chiral invariant interactions contain one- and two-pion couplings. We obtain simple relations for the coupling constants of the one- and two-pion spin-1/2-3/2 transitions terms.