Long period nodal motion of sun synchronous orbits

An approximative model is formulated for assessing these perturbations that significantly affect long term modal motion of sun synchronous orbits. Computer simulations with several independent computer programs consider zonal and tesseral gravitational harmonics, third body gravitational disturbances induced by the sun and the moon, and atmospheric drag. A pendulum model consisting of evenzonal harmonics through order 4 and solar gravity dominated nodal motion approximation. This pendulum motion results from solar gravity inducing an inclination oscillation which couples into the nodal precession induced by the earth's oblateness. The pendulum model correlated well with simulations observed flight data

Nonlinear Analysis of a Two-Parachute System Undergoing Pendulum Motion

Motion resembling that of a pendulum undergoing large-amplitude limit cycle oscillation was observed during a series of flight tests of an unoccupied Orion Capsule Parachute Assembly System (CPAS) comprised of two parachutes and a capsule payload. Large excursions away from vertical by the capsule could cause it to strike the ground or ocean at a large angle with respect to vertical, or at a large horizontal speed. These conditions are undesirable because they would endanger the occupants of the capsule in an actual mission. A simplified planar dynamics model in conjunction with a nonlinear normal force coefficient vs. angle of attack model serves as the basis of an analytical investigation of the fundamental dynamics of this pendulum motion. Output error methodology from system identification theory was used to identify the parameters of the nonlinear aerodynamics model. The identified model yielded excellent comparison with portions of flight test data where the pendulum motion occurred. Due to the inherent nonlinear nature of the pendulum motion limit cycle, traditional nonlinear analysis techniques were applied to gain further insight into the system. Lyapunovs direct method provided mathematical proof in the absolute stability of the pendulum mode. Describing Function method was used to predict the amplitude and frequency of the limit cycle oscillation. Finally, phase plane analysis allowed easy visualization on the size and shape of the limit cycle with respect to variations in key aerodynamic parameters

A computer controlled pendulum with position readout

We have designed, built and operated a physical pendulum which allows one to demonstrate experimentally the behaviour of the pendulum under any equation of motion for such a device for any initial conditions. All parameters in the equation of motion can be defined by the user. The potential of the apparatus reaches from demonstrating simple undamped harmonic oscillations to complex chaotic behaviour of the pendulum. The position data of the pendulum as well as derived kinematical quantities like velocity and acceleration can be stored for later offline analysis.Comment: 9 pages RevTeX, 9 figure

Translation of Time-Reversal Violation in the Neutral K-Meson System into a Table-Top Mechanical System

Weak interactions break time-reversal (T) symmetry in the two-state system of neutral K mesons. We present and discuss a two-state mechanical system, a Foucault-type pendulum on a rotating table, for a full representation of K0 K0bar transitions by the pendulum motions including T violation. The pendulum moves with two different oscillation frequencies and two different magnetic dampings. Its equation of motion is identical with the differential equation for the real part of the CPT-symmetric K-meson wave function. The pendulum is able to represent microscopic CP and T violation with CPT symmetry owing to the macroscopic Coriolis force which breaks the symmetry under reversal-of-motion. Video clips of the pendulum motions are shown as supplementary material.Comment: 11 pages, 5 figures, 1 external url with video clip