Earlier research has shown that students have tremendous difficulties with understanding certain aspects of rolling without slipping, such as the zero-velocity at the contact point and plausibility of application of the law of conservation of mechanical energy despite action of the friction force. The aim of this research was to explore whether using analogies and reasoning about extreme cases can facilitate conceptualization of the above-mentioned phenomena. A pre-test – post-test quasi-experiment has been conducted, with 93 students in the control group (CG) and 91 students in the experimental group (EG). Whereas control group students received conventional teaching, in the experimental group rolling of a cylinder has been considered as a special case of a tumbling prism for which the number of prism surfaces tended to infinity. The results of analysis of covariance showed that students from the experimental group significantly outperformed their peers from the control group on the Rolling Motion Concept Test (RMCT). Between-group differences were greater on test items that required higher level of cognitive transfer. This research suggests that using analogies and extreme case reasoning can facilitate comprehension of certain seemingly counterintuitive aspects of rolling motion. Keywords: analogy-based teaching, energy conservation, extreme case reasoning, misconceptions, rolling motion.

We present a theory of high-order harmonic generation by arbitrary polyatomic molecules based on the molecular strong-field approximation (MSFA) in the framework of the S-matrix theory. A polyatomic molecule is modeled by an (N + 1)-particle system, which consists of N heavy atomic (ionic) centers and an electron. We derived various versions (with or without the dressing of the initial and/or final molecular state) of the MSFA. The general expression for the T-matrix element takes a simple form for neutral polyatomic molecules. We show the existence of the interference minima in the harmonic spectrum and explain these minima as a multiple-slit type of interference. This is illustrated by numerical examples for the nitrous oxide (N2O) molecule exposed to strong linearly polarized laser field.

High-order harmonic generation by a bicircular field, which consists of two coplanar counter-rotating circularly polarized fields of frequency $r\omega$ and $s\omega$ ($r$ and $s$ are integers), is investigated for a polyatomic molecule. This field possesses dynamical symmetry, which can be adjusted to the symmetry of the molecular Hamiltonian and used to investigate the molecular symmetry. For polyatomic molecules having the $C_{r+s}$ symmetry only the harmonics $n=q(r+s)\pm r$, $q=1,2,\ldots$, are emitted having the ellipticity $\varepsilon_n=\pm 1$. We illustrate this using the example of the planar molecules BH$_3$ and BF$_3$, which obey the $C_3$ symmetry. We show that for the BF$_3$ molecule, similarly to atoms with a $p$ ground state, there is a strong asymmetry in the emission of high harmonics with opposite helicities. This asymmetry depends on the molecular orientation.

We investigate high-order above-threshold ionization (HATI) of krypton atoms by a bicircular laser field, which consists of two coplanar co- or counter-rotating circularly polarized fields of frequencies rw and sw. We show that the photoelectron spectra in the HATI process, presented in the momentum plane, exhibit the same discrete rotational symmetry as the driving field. We also analyze HATI spectra for various combinations of the intensities of two field components for co- and counter-rotating fields. We find that the appearance of high-energy plateau for the counter-rotating case is vary sensitive to the laser intensity ratio, while the plateau is always absent for the co-rotating bicircular field.