arXiv subjects

Veljko Dmitrašinović

Publications and source records attributed to Veljko Dmitrašinović.

3 recordsLinked to original sources

arXiv2023

Three-body periodic collisionless equal-mass free-fall orbits revisited

Li and Liao announced (2019) discovery of 313 periodic collisionless orbits' initial conditions (i.c.s), 30 of which have equal masses, and 18 of these 30 orbits have physical periods (scale-invariant periods) $T^{*}=T|E|^{3/2}<80$. That work left a lot to be desired, however, both in terms of logical consistency and of numerical efficiency. We have conducted a new search for periodic free-fall orbits, limited to the equal-mass case. Our search produced 24,582 i.c.s of equal-mass periodic orbits with scale-invariant period $T^{*}<80$, corresponding to 12,409 distinct solutions, 236 of which are self-dual.

physics.class-ph↗

arXiv2016

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-Henon'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 $E=-\frac12$. Upon plotting $L(T/k)$ we find that all our solutions fall on a curve that is virtually indiscernible by naked eye from the $L(T)$ curve for non-satellite solutions. The standard deviation of the satellite data from the sixth-order polynomial fit to the progenitor data is $σ= 0.13$. This regularity supports Henon's 1976 conjecture that the linearly stable Broucke-Hadjidemetriou-Henon orbits are also perpetually, or Kolmogorov-Arnold-Moser stable.

physics.class-ph↗

arXiv2016

Permutation-symmetric three-body O(6) hyperspherical harmonics in three spatial dimensions

We have constructed the three-body permutation symmetric O(6) hyperspherical harmonics which can be used to solve the non-relativistic three-body Schr{\" o}dinger equation in three spatial dimensions. We label the states with eigenvalues of the $U(1) \otimes SO(3)_{rot} \subset U(3) \subset O(6)$ chain of algebras and we present the corresponding $K \leq 4$ harmonics. Concrete transformation properties of the harmonics are discussed in some detail.

math-ph↗