Scattering of circularly polarized light by a rotating black hole

We study scattering of polarized light by a rotating (Kerr) black hole of the mass M and the angular momentum J. In order to keep trace of the polarization dependence of photon trajectories one can use the following dimensionless parameter: $\varepsilon=\pm (\omega M)^{-1}$, where $\omega$ is the photon frequency and the sign + (-) corresponds to the right (left) circular polarization. We assume that |\varepsilonl << 1 and use the modified geometric optics approximation developed in [1], that is we include the first order in $\varepsilon$ polarization dependent terms into the eikonal equation. These corrections modify late time behavior of photons. We demonstrate that the photon moves along a null curve, which in the limit $\varepsilon=0$ becomes a null geodesic. We focus on the scattering problem for polarized light. Namely, we consider the following problems: (i) How does the photon bending angle depend on its polarization; (ii) How does position of the image of a point-like source depend on its polarization; (iii) How does the arrival time of photons depend on their polarization. We perform the numerical calculations that illustrate these effects for an extremely rotating black hole and discuss their possible applications.Comment: 17 pages, 8 figure

Origami launcher

The article studies the elastic and locomotive properties of Miura-ori-type paper origami. The mechanics of a single paper crease is studied experimentally, and its non-elastic properties turn out to be crucial. The entire origami construction is then described as a collection of individual creases, its capability to launch small objects is evaluated, and the equation of motion is found. Thus, the height of the launched ball is studied theoretically and experimentally as a function of governing parameters.Comment: Accepted to the Emergent Scientis

Humanoid robot orientation stabilization by shoulder joint motion during locomotion

Arm swing action is a natural phenomenon that emerges in biped locomotion. A shoulder torque reference generation method is introduced in this paper to utilize arms of a humanoid robot during locomotion. Main idea of the technique is the employment of shoulder joint actuation torques in order to stabilize body orientation. The reference torques are computed by a method which utilizes proportional and derivative actions. Body orientation angles serve as the inputs of this system. The approach is tested via simulations with the 3D full-dynamics model of the humanoid robot SURALP (Sabanci University Robotics Research Laboratory Platform). Results indicate that the method is successful in reducing oscillations of body angles during bipedal walking

Microsoft Kinect-based differences in lower limb kinematics and temporal characteristics of sit to walking phase of modified TUG test between men with and without Parkinson's disease

http://www.ester.ee/record=b476770

On the evolution of mean motion resonances through stochastic forcing: Fast and slow libration modes and the origin of HD128311

Aims. We clarify the response of extrasolar planetary systems in a 2:1 mean motion commensurability with masses ranging from the super Jovian range to the terrestrial range to stochastic forcing that could result from protoplanetary disk turbulence. The behaviour of the different libration modes for a wide range of system parameters and stochastic forcing magnitudes is investigated. The growth of libration amplitudes is parameterized as a function of the relevant physical parameters. The results are applied to provide an explanation of the configuration of the HD128311 system. Methods. We first develop an analytic model from first principles without making the assumption that both eccentricities are small. We also perform numerical N-body simulations with additional stochastic forcing terms to represent the effects of putative disk turbulence. Results. Systems are quickly destabilized by large magnitudes of stochastic forcing but some stability is imparted should systems undergo a net orbital migration. The slow mode, which mostly corresponds to motion of the angle between the apsidal lines of the two planets, is converted to circulation more readily than the fast mode which is associated with oscillations of the semi-major axes. This mode is also vulnerable to the attainment of small eccentricities which causes oscillations between periods of libration and circulation. Conclusions. Stochastic forcing due to disk turbulence may have played a role in shaping the configurations of observed systems in mean motion resonance. It naturally provides a mechanism for accounting for the HD128311 system.Comment: 15 pages, 8 figures, added discussion in h and k coordinates, recommended for publicatio

A Unified Approach to Configuration-based Dynamic Analysis of Quadcopters for Optimal Stability

A special type of rotary-wing Unmanned Aerial Vehicles (UAV), called Quadcopter have prevailed to the civilian use for the past decade. They have gained significant amount of attention within the UAV community for their redundancy and ease of control, despite the fact that they fall under an under-actuated system category. They come in a variety of configurations. The "+" and "x" configurations were introduced first. Literature pertinent to these two configurations is vast. However, in this paper, we define 6 additional possible configurations for a Quadcopter that can be built under either "+" or "x" setup. These configurations can be achieved by changing the angle that the axis of rotation for rotors make with the main body, i.e., fuselage. This would also change the location of the COM with respect to the propellers which can add to the overall stability. A comprehensive dynamic model for all these configurations is developed for the first time. The overall stability for these configurations are addressed. In particular, it is shown that one configuration can lead to the most statically-stable platform by adopting damping motion in Roll/Pitch/Yaw, which is described for the first time to the best of our knowledge.Comment: 6 page, 9 figure

The Diver with a Rotor

We present and analyse a simple model for the twisting somersault. The model is a rigid body with a rotor attached which can be switched on and off. This makes it simple enough to devise explicit analytical formulas whilst still maintaining sufficient complexity to preserve the shape-changing dynamics essential for twisting somersaults in springboard and platform diving. With `rotor on' and with `rotor off' the corresponding Euler-type equations can be solved, and the essential quantities characterising the dynamics, such as the periods and rotation numbers, can be computed in terms of complete elliptic integrals. Thus we arrive at explicit formulas for how to achieve a dive with m somersaults and n twists in a given total time. This can be thought of as a special case of a geometric phase formula due to Cabrera 2007.Comment: 15 pages, 6 figure