Circular motion

Abstract: Near a solid boundary, Escherichia coli swims in clockwise circular motion. We provide a hydrodynamic model for this behavior. We show that circular trajectories are natural consequences of force-free and torque-free swimming and the hydrodynamic interactions with the boundary, which also leads to a hydrodynamic trapping of the cells close to the surface. We compare the results of the model with experimental data and obtain reasonable agreement. In particular, the radius of curvature of the trajectory is observed to increase with the length of the bacterium body.

Abstract: This series of two papers provides a rigorous comprehensive approach to the design of the principal software algorithmsutilized in modern-day strapdown inertial navigation systems: integration ofangular rateinto attitude, acceleration transformation/integration into velocity, and integration of velocity into position. The algorithms are structured utilizing the two-speed updating approach originally developed for attitude updating in which an analytically exact equation is used at moderate speed to update the integration parameter (attitude, velocity, or position) with input provided from a high-speed algorithm measuring dynamic angular rate/acceleration effects within the parameter update time interval [coning for attitude updating, sculling for velocity updating, and scrolling (writer’ s terminology ) for high-resolution position updating]. The algorithm design approach accounts for angular rate/specie c force acceleration measurements from the strapdown system inertial sensors as well as rotation of the navigation frame used for attitude referencing and velocity integration. This paper, Part 1, dee nes the overall design requirement for the strapdown inertial navigation integration function and develops direction cosine and quaternion forms for the attitude updating algorithms. Part 2 [Savage, P. G., “ Strapdown Inertial Navigation Integration Algorithm Design Part 2: Velocity and Position Algorithms,”Journal of Guidance, Control, and Dynamics (to be published )] deals with design of the velocity and position integration algorithms. Although Parts 1 and 2 often cover fundamental inertial navigation concepts, the material presented is intended for use by the practitioner who is already familiar with basic inertial navigation concepts.

Abstract: This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level

Abstract: This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and time-invariant or time-varying. The emphasis of this paper is to show how previous results assuming all-to-all communication can be extended to a general communication framework.

Abstract: Position sensing of movable elements including but not limited to machine components is disclosed. Motion of a movable element can produce motion of a magnetic field, which can be detected by magnetic sensors. The motion and/or variations of a magnetic field and/or a magnetic flux may be produced by any combination of a motion of the sensors, associated magnets, or associated magnetic material. Magnetic sensors may be capable of measuring either rotary, or linear motion, or both. Such sensors can provide indication of an incremental position change, an absolute position, or both. Absolute position and high-resolution position sensing may be produced for measurement of either linear and/or angular motion. Suitable magnetic sensors include, but are not limited to, Hall effect devices and/or magneto-resistive elements, and may include multi-element magnetic sensors. Suitable signal conditioning and/or control means such as control electronics can be used to receive output signals from the sensors.