Abstract. We introduce a simple and powerful procedure-the observer method-in order to obtain a reliable method of numerical integration over an arbitrary long interval of time for systems of ordinary differential equations having first integrals. This aim is achieved by a modification of the original system such that the level manifold of the first integrals becomes a local attractor. We provide a theoretical justification of this procedure. We report many tests and examples dealing with a large spectrum of systems with different dynamical behaviour. The comparison with standard and symplectic methods of integration is also provided.
Very-High Energy (VHE) gamma-ray astroparticle physics is a relatively young field, and observations over the past decade have surprisingly revealed almost two hundred VHE emitters which appear to act as cosmic particle accelerators. These sources are an important component of the Universe, influencing the evolution of stars and galaxies. At the same time, they also act as a probe of physics in the most extreme environments known -such as in supernova explosions, and around or after the merging of black holes and neutron stars. However, the existing experiments have provided exciting glimpses, but often falling short of supplying the full answer. A deeper understanding of the TeV sky requires a significant improvement in sensitivity at TeV energies, a wider energy coverage from tens of GeV to hundreds of TeV and a much better angular and energy resolution with respect to the currently running facilities. The next generation gamma-ray observatory, the Cherenkov Telescope Array Observatory (CTAO), is the answer to this need. In this talk I will present this upcoming observatory from its design to the construction, and its potential science exploitation. CTAO will allow the entire astronomical community to explore a new discovery space that will likely lead to paradigm-changing breakthroughs. In particular, CTA has an unprecedented sensitivity to short (sub-minute) timescale phenomena, placing it as a key instrument in the future of multi-messenger and multi-wavelength time domain astronomy. I will conclude the talk presenting the first scientific results obtained by the LST-1, the prototype of one CTA telescope type -the Large Sized Telescope, that is currently under commission.
In this paper, we investigate the gyrostat under influence of an external potential force with the Suslov nonholonomic constraint: the projection of the total angular velocity onto a vector fixed in the body vanishes. We investigate cases of free gyrostat, the heavy gyrostat in the constant gravity field, and we discuss certain properties for general potential forces. In all these cases, the system has two first integrals: the energy and the geometric first integral. For its integrability, either two additional first integrals or one additional first integral and an invariant $n$-form are necessary. For the free gyrostat we identify three cases integrable in the Jacobi sense. In the case of heavy gyrostat three cases with one additional first integral are identified. Among them, one case is integrable and the non-integrability of the remaining cases is proved by means of the differential Galois methods. Moreover, for a distinguished case of the heavy gyrostat a co-dimension one invariant subspace is identified. It was shown that the system restricted to this subspace is super-integrable, and solvable in elliptic functions. For the gyrostat in general potential force field conditions of the existence of an invariant $n$-form defined by a special form of the Jacobi last multiplier are derived. The class of potentials satisfying them is identified, and then the system restricted to the corresponding invariant subspace of co-dimension one appears to be integrable in the Jacobi sense.
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