angular velocity vectorの例文

• The angular velocity vector \ vec \ omega is then defined as:
• This angular motion is quantified by the angular velocity vector.
• If a disk spins counterclockwise as seen from above, its angular velocity vector points upwards.
• In the case of a frame, the angular velocity vector is over the instantaneous axis of rotation.
• As it is a Hodge dual vector, which is precisely the previous angular velocity vector \ vec \ omega:
• The angular velocity vector also points along the axis of rotation in the same way as the angular displacements it causes.
• It can be dual to get a 3 dimensional pseudovector that is precisely the previous angular velocity vector \ vec \ omega:
• There are two possible ways to describe the angular velocity of a rotating frame : the angular velocity vector and the angular velocity tensor.
• Thus, the magnitude of the angular velocity vector at a given time " t " is consistent with the two dimensions case.
• Using the unit vector \ bold u defined before, the angular velocity vector may be written in a manner similar to that for two dimensions:
• The minus sign arises from the traditional definition of the cross product ( right hand rule ), and from the sign convention for angular velocity vectors.
• The addition of angular velocity vectors for frames is also defined by movement composition, and can be useful to decompose the movement as in a gimbal.
• The angular kinetic energy may be expressed in terms of the moment of inertia tensor \ mathbf { I } and the angular velocity vector \ boldsymbol \ omega
• The vorticity vector would be twice the mean angular velocity vector of those particles relative to their center of mass, oriented according to the right-hand rule.
• In a vortex, in particular, \ vec \ omega may be opposite to the mean angular velocity vector of the fluid relative to the vortex's axis.
• This construction describes the motion of the angular velocity vector \ mathbf { \ omega } of a rigid body with one point fixed ( usually its center of mass ).
• Steady flight is defined as flight where the aircraft's linear and angular velocity vectors are constant in a body-fixed reference frame such as the body frame or wind frame.
• To relate these constraints, we note that the gradient vector of the kinetic energy with respect to angular velocity vector \ boldsymbol \ omega equals the angular momentum vector \ mathbf { L}
• To maintain rotation around a fixed axis, the total torque vector has to be along the axis, so that it only changes the magnitude and not the direction of the angular velocity vector.
• The local rotation measured by the vorticity \ vec \ omega must not be confused with the angular velocity vector of that portion of the fluid with respect to the external environment or to any fixed axis.