A proof for the angular velocity parallelogram

A Neural Circuit for Angular Velocity Computation

In one of the most remarkable feats of motor control in the animal world, some Diptera, such as the housefly, can accurately execute corrective flight maneuvers in tens of milliseconds. These reflexive movements are achieved by the halteres, gyroscopic force sensors, in conjunction with rapidly tunable wing steering muscles. Specifically, the mechanosensory campaniform sensilla located at the b...

Integrating rotation from angular velocity

The integration of the rotation from a given angular velocity is often required in practice. The present paper explores how the choice of the parametrization of rotation, when employed in conjuction with different numerical time-integration schemes, effects the accuracy and the computational efficiency. Three rotation parametrizations – the rotational vector, the Argyris tangential vector and t...

Numerical study on the jet dynamic through centrifuge spinning: influence of angular velocity

The velocity and angular momentum of a free Dirac electron

It is shown that, in Dirac theory, there is a spatial velocity of a free electron which commutes with the Hamiltonian, so it is a conserved quantity of the motion. Furthermore, there is a spatial orbital angular momentum which also commutes with the Hamiltonian and is a constant of the motion.

A new proof for the Banach-Zarecki theorem: A light on integrability and continuity

To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...