On the uniqueness of limit cycles for Li\'enard equation: the legacy of G. Sansone

We give an account of the results about limit cycle's uniqueness for Li\'enard equations, from Levinson-Smith's one to the most recent ones. We present a new uniqueness theorem in the line of Sansone-Massera's geometrical approach.Comment: 2 figure

Finding Hamiltonian isochronous centers by non-canonical transformations

Starting from a class of isochronous Hamiltonian centers, we produce a new class of Hamiltonian isochronous centers by using non-canonical transformations

Limit cycle's uniqueness for a class of planar dynamical systems

A uniqueness theorem for limit cycles of a class of plane differential system is proved. The main result is applicable to secord order O.D.E.'s with dissipative term depending both on the position and the velocity

New techniques for laser beam atmospheric extinction measurements from manned and unmanned aerospace vehicles

Novel techniques for laser beam atmospheric extinction measurements, suitable for several air and space platform applications, are presented in this paper. Extinction measurements are essential to support the engineering development and the operational employment of a variety of aerospace electro-optical sensor systems, allowing calculation of the range performance attainable with such systems in current and likely future applications. Such applications include ranging, weaponry, Earth remote sensing and possible planetary exploration missions performed by satellites and unmanned flight vehicles. Unlike traditional LIDAR methods, the proposed techniques are based on measurements of the laser energy (intensity and spatial distribution) incident on target surfaces of known geometric and reflective characteristics, by means of infrared detectors and/or infrared cameras calibrated for radiance. Various laser sources can be employed with wavelengths from the visible to the far infrared portions of the spectrum, allowing for data correlation and extended sensitivity. Errors affecting measurements performed using the proposed methods are discussed in the paper and algorithms are proposed that allow a direct determination of the atmospheric transmittance and spatial characteristics of the laser spot. These algorithms take into account a variety of linear and non-linear propagation effects. Finally, results are presented relative to some experimental activities performed to validate the proposed techniques. Particularly, data are presented relative to both ground and flight trials performed with laser systems operating in the near infrared (NIR) at ?= 1064 nm and ?= 1550 nm. This includes ground tests performed with 10 Hz and 20 KHz PRF NIR laser systems in a large variety of atmospheric conditions, and flight trials performed with a 10 Hz airborne NIR laser system installed on a TORNADO aircraft, flying up to altitudes of 22,000 ft

Novel atmospheric extinction measurement techniques for aerospace laser system applications

Novel techniques for laser beam atmospheric extinction measurements, suitable for manned and unmanned aerospace vehicle applications, are presented in this paper. Extinction measurements are essential to support the engineering development and the operational employment of a variety of aerospace electro-optical sensor systems, allowing calculation of the range performance attainable with such systems in current and likely future applications. Such applications include ranging, weaponry, Earth remote sensing and possible planetary exploration missions performed by satellites and unmanned flight vehicles. Unlike traditional LIDAR methods, the proposed techniques are based on measurements of the laser energy (intensity and spatial distribution) incident on target surfaces of known geometric and reflective characteristics, by means of infrared detectors and/or infrared cameras calibrated for radiance. Various laser sources can be employed with wavelengths from the visible to the far infrared portions of the spectrum, allowing for data correlation and extended sensitivity. Errors affecting measurements performed using the proposed methods are discussed in the paper and algorithms are proposed that allow a direct determination of the atmospheric transmittance and spatial characteristics of the laser spot