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Related Concept Videos

Rotation with Constant Angular Acceleration - II01:16

Rotation with Constant Angular Acceleration - II

Kinematics is the description of motion. The kinematics of rotational motion discusses the relationships between rotation angle, angular velocity, angular acceleration, and time. One can describe many things with great precision using kinematics, but kinematics does not consider causes. For example, a large angular acceleration describes a very rapid change in angular velocity without any consideration of its cause. Thus, rotational kinematics does not represent the laws of nature.
The first...
Orthogonal Trajectories01:26

Orthogonal Trajectories

Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
Rotation with Constant Angular Acceleration - I01:37

Rotation with Constant Angular Acceleration - I

If angular acceleration is constant, then we can simplify equations of rotational kinematics, similar to the equations of linear kinematics. This simplified set of equations can be used to describe many applications in physics and engineering where the angular acceleration of a system is constant.
Using our intuition, we can begin to see how rotational quantities such as angular displacement, angular velocity, angular acceleration, and time are related to one another. For example, if a flywheel...
Angular Momentum about an Arbitrary Axis01:11

Angular Momentum about an Arbitrary Axis

Imagine a rigid body with a mass denoted as 'm', which has its center of mass at point G and is rotating around an inertial reference frame. The angular momentum at an arbitrary point P can be calculated by taking the cross product of the position vector and linear momentum vector for each individual mass element.
The velocity of a mass element comprises its translational velocity and the relative velocity instigated by the body's rotation. Substituting the velocity equation into the angular...
Gyroscope: Precession01:24

Gyroscope: Precession

Precession can be demonstrated effectively through a spinning top. If a spinning top is placed on a flat surface near the surface of the Earth at a vertical angle and is not spinning, it will fall over due to the force of gravity producing a torque acting on its center of mass. However, if the top is spinning on its axis, it precesses about the vertical direction, rather than topple over due to this torque. Precessional motion is a combination of a steady circular motion of the axis and the...
Relative Motion Analysis using Rotating Axes01:25

Relative Motion Analysis using Rotating Axes

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it instrumental in...

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Related Experiment Video

Updated: Jun 27, 2026

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

An auto-calibrated, angularly continuous, two-dimensional GRAPPA kernel for propeller trajectories.

Stefan Skare1, Rexford D Newbould, Anders Nordell

  • 1Lucas MRS/I Center, Department of Radiology, Stanford University, Stanford, CA 94305, USA. stefan@skare.se

Magnetic Resonance in Medicine
|November 26, 2008
PubMed
Summary
This summary is machine-generated.

This study explores parallel imaging (PI) for faster MRI scans using propeller sequences. An improved GRAPPA kernel method enhances image quality and stability from undersampled data.

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Published on: December 10, 2014

Area of Science:

  • Magnetic Resonance Imaging (MRI)
  • Medical Imaging Physics

Background:

  • Propeller-type MRI sequences offer benefits like reduced blurring and specific absorption ratio (SAR) reduction.
  • EPI-based propeller methods (Turbo-PROP, SAP-EPI) accelerate k-space traversal, mitigating geometric distortions.

Purpose of the Study:

  • To investigate the feasibility of calculating a 2D GRAPPA kernel using only undersampled propeller blades.
  • To develop a more numerically stable GRAPPA kernel estimation for propeller MRI.

Main Methods:

  • Explored calculating a 2D GRAPPA kernel on undersampled propeller blades using matching orthogonal blades.
  • Proposed an angularly continuous 2D GRAPPA kernel formulation with parameterized angular variation.

Main Results:

  • Demonstrated that the GRAPPA kernel exhibits slow variation across blades.
  • The proposed angularly continuous kernel significantly improved numerical stability in GRAPPA weight estimation.

Conclusions:

  • The novel kernel formulation enables the generation of fully sampled, diagnostic quality images from undersampled propeller data.
  • This method enhances the efficiency and robustness of parallel imaging in propeller MRI acquisitions.