Force fictitious

The first pseudo force, Fi, is called the Coriolis force, and its magnitude is directly proportional to the angular velocity of the rotating frame of reference and the linear velocity of the particle in this frame. By definition, this force is perpendicular to the plane where vectors Vi and o are located, Fig. 2.3a, and depends on the mutual position of these vectors. The second fictitious force, F2, is called the centrifugal force. Its magnitude is directly proportional to the square of the angular velocity and the distance from the particle to the center of rotation. It is directed outward from the center and this explains the name of the force. It is obvious that with an increase of the angular velocity the relative contribution of this force... 

When performing variable-cell AIMD simulations with plane-wave basis sets, problems originate from the fact that the basis set is not complete with respect to the cell vectors.71 This incompleteness can introduce fictitious forces (Pulay forces) into asys and lead to artificial dynamics. To overcome this problem, one must ensure that asys is well converged with respect to the basis set size. In general, it is found that one needs to employ a plane-wave kinetic... 

Centrifugal force. When a non-inertial rotating coordinate system is used to analyze motion, Newton s law F = ma is not correct unless one adds to the real forces a fictitious force called the centrifugal force. The centrifugal force required in the non-inertial system is equal and opposite to the centripetal force calculated in the inertial system. Since the centrifugal and centripetal forces... 

The fictitious forces are conventionally derived with the help of the framework of classical mechanics of a point particle. Newtonian mechanics recognizes a special class of coordinate systems called inertial frames. The Newton s laws of motion are defined in such a frame. A Newtonian frame (sometimes also referred to as a fixed, absolute or absolute frame) is undergoing no accelerations and conventionally constitute a coordinate system at rest with respect to the fixed stars or any coordinate system moving with constant velocity and without rotation relative to the inertial frame. The latter concept is known as the principle of Galilean relativity. Speaking about a rotating frame of reference we refer to a coordinate system that is rotating relative to an inertial frame. 

It turns out that two fictitious forces occur in the momentum equation when written in cylindrical coordinates. The term pmeVrlr is an effective force in the 0-direction when there is flow in both the r- and 0-directions. The term pvg jr gives the effective force in the r-direction resulting from fluid motion in the 0-direction. These terms do not represent the familiar Coriolis and centrifugal forces due to the earth s rotation. Instead, they arise automatically on transformation of the momentum equations from Cartesian to cylindrical coordinates and are thus not added on physical grounds (kinematics). Nevertheless, the pv /r term is sometimes referred to as a Coriolis force and the pv gjr term is often called a centrifugal force. It is thus important to distinguish between the different types of fictitious forces. 

The components of these fictitious forces are usually added to the body force g of momentum equation components (7.91) to (7.93). For the different components of the momentum equation we get ... 

If the variable in the extended Lagrangian is taken to be the Gaussian width factor Q, one obtains the fictitious force [6]... 

Note that if the constraint would be elastic, the gyristors (GR) would stay in the model and represent the fictitious forces like the centrifugal force (in case of a rigid constraint, the corresponding velocity and thus the corresponding power is zero, such that the contribution becomes irrelevant for the behavior). 

There is also a Coriolis force that vanishes as the body s velocity in the rotating local frame approaches zero. The centrifugal and Coriohs forces are apparent or fictitious forces, in the sense that they are caused by the acceleration of the rotating frame rather than by interactions between particles. When we treat these forces as if they are real forces, we can use Newton s second law of motion to relate the net force on a body and the body s acceleration in the rotating frame (see Sec. G.6). 

In the calculation of work with Eqs. G.6.9-G.6.11, we do not include forces from an external field such as a gravitational field, or fictitious forces Fy if present. 

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