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Y W is the weak hypercharge – the generator of the U(1) group, W → μ is the 3-component SU(2) gauge field, L are the Pauli matrices – infinitesimal generators of the SU(2) group – with subscript L to indicate that they only act on left-chiral fermions, g' and g are the U(1) and SU(2) coupling constants respectively,
Linear motion, also called rectilinear motion, [1] is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion , with constant velocity (zero acceleration ); and non-uniform linear motion , with variable velocity ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
The image to the right shows the amount of elapsed time before the pendulum flips over, as a function of initial position when released at rest. Here, the initial value of θ 1 ranges along the x-direction from −3.14 to 3.14. The initial value θ 2 ranges along the y-direction, from −3.14 to 3.14. The color of each pixel indicates whether ...
The space R 3 is endowed with a scalar product , . Time is a scalar which is the same in all space E 3 and is denoted as t. The ordered set { t} is called a time axis. Motion (also path or trajectory) is a function r : Δ → R 3 that maps a point in the interval Δ from the time axis to a position (radius vector) in R 3.
Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space.This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession.
The following is a simplistic illustrated explanation of how motion compensation works. Two successive frames were captured from the movie Elephants Dream.As can be seen from the images, the bottom (motion compensated) difference between two frames contains significantly less detail than the prior images, and thus compresses much better than the rest.
Motion vectors that result from a movement into the -plane of the image, combined with a lateral movement to the lower-right.This is a visualization of the motion estimation performed in order to compress an MPEG movie.