2 papers
math.NA2025
An explicit integrator uniform in the true anomaly and exactly preserving all integrals of motion in the three-dimensional Kepler problem
Jan L. Cieśliński, Maciej Jurgielewicz
We develop a numerical scheme for the Kepler problem that preserves exactly all first integrals: angular momentum, total energy, and the Laplace-Runge-Lenz vector. This property en…
math.HO2023
On geometric interpretation of Euler's substitutions
Jan L. Cieśliński, Maciej Jurgielewicz
We consider a classial case of irrational integrals containing a square root of a quadratic polynomial. It is well known that they can be expressed in terms of elementary functions…