The equations of motion of a two-degrees-of-freedom mass in a magnetic bearing are non-linear in displacement, with geometric coupling of the magnetic bearing coupling the horizontal and vertical components of rotor motion. The non-linear forced response is studied in two ways: (1) using imbalance force; (2) using non-imbalance harmonic force. In the forced response, only periodic motion is inv...

We consider an ion whose motion is con®ned to a plane perpendicular to a constant magnetic ®eld. A harmonic trapping ®eld is applied within the plane of the ion’s motion, together with some unspeci®ed irradiating probe beam. By determining the dynamics of the ion we show that the particle theory is formally equivalent to that of a coupled massive ...1‡ 2†-dimensional vector Boson ®eld. The ®eld...

Simulation results on dynamic yaw stability derivatives of a gull bird by means of computational fluid dynamics are presented. Two different kinds of motions are used for determining the dynamic yaw stability derivatives Nr C and β& N C . Concerning the first one, simple lateral translation and yaw rotary motions in yaw are considered. The second one consists of combined motions. To determine d...

The rotational motion of an iSN nitroxide in diisobutylphthalate solutions at varied temperatures has been studied for correlation times from 1Om8 to > 10m3 sec. Data from both conventional (first-harmonic, in-phase) and saturation-transfer (second-harmonic, out-of-phase) EPR are reported. For many spectral parameters, including linewidth, position of outer extrema, and ratios of spectral ampli...

A trajectory of a harmonic oscillator obeying the Schrödinger wave equation is exactly derived and illustrated. The trajectory resembles well the classical orbit between the turning points, and also runs through the tunneling region. The dynamics of the ‘particle’ motion and the wave function associated with the motion are proposed. The period of a round trip on the trajectory is exactly equal ...

We search for nonlinear effects in nuclear giant resonances (GRs), in particular the isovector dipole and the isoscalar quadrupole modes. To that end, we employ a spectral analysis of time-dependent Hartree-Fock (TDHF) dynamics using Skyrme forces. Based on TDHF calculations over a wide range of excitation amplitudes, we explore the collectivity and degree of harmonic motion in these modes. Bot...

We analytically and numerically investigate an anharmonic propagation of two-dimensional beams in a harmonic potential. We pick noncentrosymmetric beams of common interest that carry orbital angular momentum. The examples studied include superposed Bessel-Gauss (BG), Laguerre-Gauss (LG), and circular Airy (CA) beams. For the BG beams, periodic inversion, phase transition, and rotation with peri...

Condenser microphones of all types are traditionally made with a planar electrode parallel to an electrically conducting diaphragm, additional diaphragm stiffness at acoustic frequencies being provided by the air enclosed in a cavity behind the diaphragm. In all designs, the motion of the diaphragm in response to an acoustic signal is greatest near its center and reduces to zero at its edges. A...

In a large proton storage ring the particles circulate on narrowly defined orbits for many ~ hours, and undergo about 1012 interactions with nonlinear magnetic fields. The nonlinear fields -include significant high multipoles from inevitable errors in the fabrication of superconducting magnets. In a first approximation one neglects collective and dissipative effects, and assumes that magnetic f...

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the consta...