## March 27th, 2021

### Монодромия

Возможно, пригодится для моих хаотический упражнений...

A semi-theoretical method to detect classical monodromy: https://arxiv.org/abs/2103.13711

Juan J. Omiste, Rosario González-Férez, Rafael Ortega
An integrable Hamiltonian system presents monodromy if the action-angle variables cannot be defined globally. We consider a classical system with azimuthal symmetry and explore the topology structure of its phase space. Based on the behavior of closed orbits around singular points or regions of the energy-momentum plane, a semi-theoretical method is derived to detect classical monodromy. The validity of the monodromy test is numerically illustrated for several systems with azimuthal symmetry.

### Педагогическое об описании движения симметрического волчка

Why do we use constants of motion while studying the motion of a heavy symmetric top? https://arxiv.org/abs/2103.13984
Vedat Tanriverdi
While studying the motion of a heavy symmetric top, in general, constants of motion are used. Some students may want to understand the motion in terms of torque, which can lie on their routine based on the usage of Newton's second law. However, this is not easy.
In this work, first, we will show the equivalence of torque-angular momentum relation and Euler equations for a heavy symmetric top. Both of these give the description of the motion in terms of torque. Then, we will study some simple motions of a heavy symmetric top in terms of torque, angular momentum, angular velocities and accelerations, which can help students in understanding rigid body rotations and the necessity of considering the motion of a heavy symmetric top in terms of constants. We will also study Perry's historical observational principle on the relation between precession and the rise of the top.