Reference Frames, Body Motion and Notation

It is known that the brain uses multiple reference frames to code spatial information, including eye-centered and body-centered frames. When we move our body in space, these internal representations are no longer in register with external space, unless they are actively updated. Whether the brain updates multiple spatial representations in parallel, or whether it restricts its updating mechanisms to a single reference frame from which other representations are constructed, remains an open question. We developed an optimal integration model to simulate the updating of visual space across body motion in multiple or single reference frames. To test this model, we designed an experiment in which participants had to remember the location of a briefly presented target while being translated sideways. The behavioral responses were in agreement with a model that uses a combination of eye- and body-centered representations, weighted according to the reliability in which the target location is stored and updated in each reference frame. Our findings suggest that the brain simultaneously updates multiple spatial representations across body motion. Because both representations are kept in sync, they can be optimally combined to provide a more precise estimate of visual locations in space than based on single-frame updating mechanisms.

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Flexible Multibody Dynamics Based on a Fully Cartesian System of Support Coordinates

Journal of Mechanical Design ◽

10.1115/1.2919191 ◽

1993 ◽

Vol 115 (2) ◽

pp. 294-299 ◽

Cited By ~ 11

Author(s):

N. Vukasovic ◽

J. T. Celigu¨eta ◽

J. Garci´a de Jalo´n ◽

E. Bayo

Keyword(s):

Multibody Dynamics ◽

Reference Frames ◽

Deformable Body ◽

Equations Of Motion ◽

Flexible Multibody Dynamics ◽

Body Motion ◽

Cartesian System ◽

Flexible Multibody ◽

Local Reference ◽

Rigid Multibody

In this paper we present an extension to flexible multibody systems of a system of fully cartesian coordinates previously used in rigid multibody dynamics. This method is fully compatible with the previous one, keeping most of its advantages in kinematics and dynamics. The deformation in each deformable body is expressed as a linear combination of Ritz vectors with respect to a local frame whose motion is defined by a series of points and vectors that move according to the rigid body motion. Joint constraint equations are formulated through the points and vectors that define each link. These are chosen so that a minimum use of local reference frames is done. The resulting equations of motion are integrated using the trapezoidal rule combined with fixed point iteration. An illustrative example that corresponds to a satellite deployment is presented.

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Physics and Geometry

Introduction to Modern Dynamics ◽

10.1093/oso/9780198844624.003.0001 ◽

2019 ◽

pp. 3-52

Author(s):

David D. Nolte

Keyword(s):

Path Length ◽

Reference Frames ◽

Metric Spaces ◽

Complex Dynamics ◽

Geometric Approach ◽

Body Motion ◽

Visualization Tool ◽

Coordinate Transformations ◽

Flow Equations ◽

Rotating Frames

This chapter emphasizes the importance of a geometric approach to dynamics. The central objects of interest are trajectories of a dynamical system through multidimensional spaces composed of generalized coordinates. Trajectories through configuration space are parameterized by the path length element, which becomes an important feature in later chapters on relativity and metric spaces. Trajectories through state space are defined by mathematical flow equations whose flow fields and flow lines become the chief visualization tool for complex dynamics. Coordinate transformations and Jacobian matrices are used throughout this text, and the transformation to noninertial frames introduces fictitious forces like the Coriolis force that are experienced by observers in noninertial frames. Uniformly rotating frames provide the noninertial reference frames for the description of rigid-body motion.

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A Fully Coupled Flow and 6-DOF Motion Solver in Multiple Reference Frames

Volume 1: Symposia ◽

10.1115/ajkfluids2015-3210 ◽

2015 ◽

Author(s):

Hua Shan ◽

Sung-Eun Kim ◽

Bong Rhee

Keyword(s):

Reference Frames ◽

Inertial Frame ◽

Equations Of Motion ◽

Body Motion ◽

Governing Equations ◽

Flow Equations ◽

Fixed Frame ◽

Actuator Disk ◽

Multiple Reference Frames ◽

Multiple Reference

In many computational fluid dynamics (CFD) applications involving a single rotating part, such as the flow through an open water propeller rotating at a constant rpm, it is convenient to formulate the governing equations in a non-inertial rotating frame. For flow problems consisting of both stationary and rotating parts, e.g. the stator and the rotor of a turbine, or the hull and propeller of a ship, the multiple reference frames (MRF) approach has been widely used. In most existing MRF models, the computation domain is divided into stationary and rotating zones. In the stationary zone, the flow equations are formulated in the inertial frame, while in the rotating zone, the equations are solved in the non-inertial rotating frame. Also, the flow is assumed to be steady in both zones and the flow solution in the rotating zone can be interpreted as the phase-locked time average result. Compared with other approaches, such as the actuator disk (body-force) model, the MRF approach is superior because it accounts for the actual geometry of the rotating part, e.g. propeller blades. A more complicated situation occurs when the flow solver is coupled to the six degrees of freedom (6-DOF) equations of rigid-body motion in predicting the maneuver of a self-propelled surface or underwater vehicle. In many applications, the propeller is replaced by the actuator disk model. The current work attempts to extend the MRF approach to the 6-DOF maneuvering problems. The governing equations for unsteady incompressible flow in a non-inertial frame have been extended to the flow equations in multiple reference frames: a hull-fixed frame that undergoes translation and rotation predicted by the 6-DOF equations of motion and a propeller-fixed frame in relative rotation with respect to the hull. Because of the large disparity between time scales in the 6-DOF rigid body motion of the hull and the relative rotational motion of the propeller, the phase-locked solution in the propeller MRF zone is considered a reasonable approximation for the actual flow around the propeller. The flow equations are coupled to the 6-DOF equations of motion using an iterative coupling algorithm. The coupled solver has been developed as part of NavyFOAM. The theoretical framework and the numerical implementation of the coupled solver are outlined in this paper. Some numerical test results are also presented.

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The Applicability of the Floating-Frame Based Component Mode Synthesis to High-Speed Rotors

Volume 4: 8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A and B ◽

10.1115/detc2011-47800 ◽

2011 ◽

Cited By ~ 1

Author(s):

Astrid Pechstein ◽

Daniel Reischl ◽

Johannes Gerstmayr

Keyword(s):

High Speed ◽

Reference Frames ◽

Rotor Dynamics ◽

Component Mode Synthesis ◽

Body Motion ◽

Fully Nonlinear ◽

Numerical Studies ◽

Nonlinear Transient ◽

Floating Frame ◽

Accuracy Of Results

The floating frame of reference formulation (FFRF) together with modal reduction is a standard method in multibody system dynamics. As an advantage of the FFRF, fully nonlinear coupling of small flexible deformations superimposed to arbitrarily large rigid body motion is considered. The idea of the present paper is to apply the FFRF with component mode synthesis to an electromagnetically levitated high-speed rotor, in which large tilting angles may occur, which are not accounted for in classical rotor dynamics. The applicability of FFRF to rotor dynamics, especially close to bending resonance, is not studied in detail in the literature. Thus, fully nonlinear and transient finite element computations are compared to different FFRF-based simulations. In exhaustive numerical studies of a flexible two-disc rotor, comparing FFRF and fully nonlinear transient computations, it is shown that the choice of reference frames and the rotation parameterization influence accuracy of results and CPU-performance.

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PIV Measurement and CFD Simulation of Liquid-Liquid Mixing in Mixer Settler with Rigid-Flexible Impeller

International Journal of Chemical Reactor Engineering ◽

10.1515/ijcre-2019-0065 ◽

2019 ◽

Vol 17 (11) ◽

Author(s):

Deyin Gu ◽

Zuohua Liu ◽

Chuanlin Xu ◽

Changyuan Tao ◽

Yundong Wang

Keyword(s):

Flow Field ◽

Reference Frames ◽

Cfd Simulation ◽

Continuous Phase ◽

Body Motion ◽

Two Phase ◽

Piv Measurement ◽

Mixing Chamber ◽

Impeller Type ◽

Multi Body

Abstract Particle image velocimetry (PIV) was used to measure the flow field in the mixing chamber of a mixer settler. An Eulerian-Eulerian approach, standard k-ε turbulence model, and multiple reference frames (MRF) technique were employed to simulate liquid-liquid two-phase flow, turbulent flow, and impeller rotation in the mixer settler, respectively. The effects of impeller type, impeller clearance and baffle configuration on the flow field were analyzed. Results showed that rigid-flexible impeller can spread the impeller energy more uniformly in the mixing chamber and increase the velocity of the continuous phase through the multi-body motion of flexible sheet compared with rigid impeller. The flow numbers of RF-RT, RF-PBT and RF-CBT systems were increased by 46 %, 54 % and 43 %, respectively, compared with RT, PBT and CBT systems. Meanwhile, the suction capacity of impeller was enhanced with a decreased impeller clearance, and the backflow was eliminated by the installation of baffles.

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