Slalom solutions

Slalom solutions are found by Šuvakov and Dmitrašinović in 2013.

• Šuvakov, M., Dmitrašinović, V., Three classes of Newtonian three-body planar periodic orbits, Phys. Rev. Lett. 110(11), 114301 (2013)
• Šuvakov, M., Dmitrašinović, V., A guide to hunting periodic three-body orbits, Am. J. Phys. 82, 609–619 (2014)
• Šuvakov, M., Numerical search for periodic solutions in the vicinity of the figure-eight orbit: slaloming around singularities on the shape sphere, Celest. Mech. Dyn. Astron. 119, 369–377 (2014)
• Šuvakov, M., Shibayama, M., Three topologically nontrivial choreographic motions of three bodies, Celest Mech Dyn Astron. 124, 155--162 (2016)

Slalom solutions are solutions to the equation of motion in planar three-body problem with equal masses. They are periodic and choreographic. Namely, three bodies chase each other on a single orbit with equal time delay.

periodic: q_k(t+T)=q_k(t) for k=0,1,2, T is the period.
choreographic: q_0(t) = q(t), q_1(t) = q(t+T/3), q_2(t)=q(t-T/3).

In my talk at MCA 2017, I treated three slalom solutions S1, S2 and S3 that have the same homotopy as 5 times iterations of figure-eight. The solutions S1, S2, S3 represent the solutions No. 3, 2, 4 respectively in Table 1 of the paper by Šuvakov and Shibayama 2016.

S1	S2	S3