Quaternion methods and models of regular celestial mechanics and astrodynamics

This paper is a review, which focuses on our work, while including an analysis of many works of other researchers in the field of quaternionic regularization. The regular quaternion models of celestial mechanics and astrodynamics in the Kustaanheimo-Stiefel (KS) variables and Euler (Rodrigues-Hamilton) parameters are analyzed. These models are derived by the quaternion methods of mechanics and are based on the differential equations of the perturbed spatial two-body problem and the perturbed spatial central motion of a point particle. This paper also covers some applications of these models. Stiefel and Scheifele are known to have doubted that quaternions and quaternion matrices can be used efficiently to regularize the equations of celestial mechanics. However, the author of this paper and other researchers refuted this point of view and showed that the quaternion approach actually leads to efficient solutions for regularizing the equations of celestial mechanics and astrodynamics.This paper presents convenient geometric and kinematic interpretations of the KS transformation and the KS bilinear relation proposed by the present author. More general (compared with the KS equations) quaternion regular equations of the perturbed spatial two-body problem in the KS variables are presented. These equations are derived with the assumption that the KS bilinear relation was not satisfied. The main stages of the quaternion theory of regularizing the vector differential equation of the perturbed central motion of a point particle are presented, together with regular equations in the KS variables and Euler parameters, derived by the aforementioned theory. We also present the derivation of regular quaternion equations of the perturbed spatial two-body problem in the Levi-Civita variables and the Euler parameters, developed by the ideal rectangular Hansen coordinates and the orientation quaternion of the ideal coordinate frame.This paper also gives new results using quaternionic methods in the perturbed spatial restricted three-body problem.

Motion sickness and sense of presence in a virtual reality environment developed for manual wheelchair users, with three different approaches

Visually Induced Motion Sickness (VIMS) is a bothersome and sometimes unsafe experience, frequently experienced in Virtual Reality (VR) environments. In this study, the effect of up to four training sessions to decrease VIMS in the VR environment to a minimal level was tested and verified through explicit declarations of all 14 healthy participants that were recruited in this study. Additionally, the Motion Sickness Assessment Questionnaire (MSAQ) was used at the end of each training session to measure responses to different aspects of VIMS. Total, gastrointestinal, and central motion sickness were shown to decrease significantly by the last training session, compared to the first one. After acclimatizing to motion sickness, participants’ sense of presence and the level of their motion sickness in the VR environment were assessed while actuating three novel and sophisticated VR systems. They performed up to four trials of the Illinois agility test in the VR systems and the real world, then completed MSAQ and Igroup Presence Questionnaire (IPQ) at the end of each session. Following acclimatization, the three VR systems generated relatively little motion sickness and high virtual presence scores, with no statistically meaningful difference among them for either MSAQ or IPQ. Also, it was shown that presence has a significant negative correlation with VIMS.

The Reception of American Cinema in Japan

Since the 1890s, Japanese movie-goers have engaged American cinema in a wide consumer marketplace shaped by intense media competition. Early fandom grew around educated urban audiences, who avidly patronized action-packed serials and Universal’s freshly imported films in the 1910s. During the 1920s and 1930s, U.S. cinema continued to attract metropolitan consumers but struggled in the face of Japan’s soaring narrative output. In the years following World War II, movie-goers encountered American films in big cities as well as provincial communities through the Occupation-backed Central Motion Picture Exchange. After the Occupation, U.S. film consumption began to slow down in theaters because of Japanese cinematic competition, but the sites of reception extended into television. The momentum of American cinema revived on the big screen with the rise of the blockbuster, though the years after the 1970s witnessed an intense segmentation of consumer taste. While U.S. cinema culture has become widely available via television, amusement parks, consumer merchandise, and the Internet, the contemporary era has seen renewed challenges mounted by domestic productions and alternative sources of popular entertainment.

Periodic Solutions of Systems with Singularities of Repulsive Type

Motivated by the classical Coulomb central motion model, we study the existence of T-periodic solutions for the nonlinear second order system of singular ordinary differential equations u′′ + g(u) = p(t). Using topological degree methods, we prove that when the nonlinearity g : ℝ

Comparison of Ganglion Cell Signals and Psychophysical Localization of Moving Targets Can Help Define Central Motion Mechanisms

Vernier acuity thresholds can be related to visibility of targets. This is considered in relation to retinal signals. Spatial precision of macaque ganglion cell responses to moving targets was assessed by neurometric analysis and compared with psychophysical performance. Under some conditions the amplitude of ganglion cell signals per se may relate target visibility to spatial precision of psychophysical performance. Other conditions are more complex; we suggest central mechanisms may adapt their properties, eg their dimensions, depending on the stochastic properties of ganglion cell signals. Thus, the relation of Vernier acuity to the visibility of targets is a rule of thumb which has a complex relation to physiological substrates.

Lifting multi-blade flows with interaction

Planar flow past multiple successive blades and wakes is studied for nearly aligned configurations with normal non-symmetry inducing lift. The typical blade lies relatively near the centreline of the oncoming wake from the preceding blade. The central motion over a wide parameter range is in condensed periodic boundary layers and wakes with fixed displacement, buried within surrounding incident shear flow. This is accompanied, however, by streamwise jumps in the pressure, velocity and mass flux, across the leading edge of each blade, a new and surprising feature which is supported by the combination of incident shears and a solid surface and which is related to the normal flow through the multi-blade system. The leading-edge jumps are required in order to satisfy the equi-pressure condition at the trailing edge. Computational results include separating flows and show the lift and drag, and these are followed by a short-blade analysis which captures the main flow properties explicitly. The results agree qualitatively with experiments and direct simulations for rotor blade flows. The jump feature also extends for example to a single blade immersed in the relatively large wake of an upstream blade.