Search results for "Angular frequency"
showing 4 items of 4 documents
Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part II: Theoretical aspects in the case of vertical …
1991
If a ball is viewed as a rigid body, its flight in the atmosphere can be described by a system of six ordinary differential equations, which has been derived in the first part of this paper. In this following second part, the theoretical aspects such as the curvature of the orbit and certain velocity functions will be investigated in the case of the vertical angular frequency of the rotating ball, in which the differential equations reduce to a planar dynamical system. This system turns out to be not explicity solvable. The solutions of the corresponding ordinary or boundary value problems. computed numerically, are used to treat certain problems in international ball games. for example, th…
Tests for real and complex unit roots in vector autoregressive models
2014
The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues +/-1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Al…
Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular freq…
1995
If a ball is viewed as a rigid body, its flight in the atmosphere can be described by six ordinary differential equations, which has been derived in the first part of this paper. In this following third part, some further theoretical aspects in the case of vertical angular frequency will be pointed out using an unknown transformation of the original independent variable, i.e. the time, as indicated in Part II. Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is given as well as—if the equations are viewed as a three-dimensional dynamical system—the unique stable equilibrium, which depends on the spin. This equilibri…
Harmonic generation from nanorings driven by a two-color laser field
2014
We study the high harmonic generation and the polarization of the harmonics emitted by a nanoring driven by two laser fields of angular frequency ?1 and ?2, with ?2?=?2?1, and ?1 resonant between the ground and the first excited state. We show that by varying parameters, such as laser intensity, photon energy and the delay between the two laser pulses, we can control the number of harmonics and the polarization of the radiation. In particular we show that with this choice of two-laser photon frequency rate we obtain more harmonics with respect to other configurations. We also calculated the average absorbed energy and the average angular momentum acquired by the electron as a function of th…