an attempt is made to show in a straightforward way how a body-fixed frame may be constructed in classical and hence in quantum mechanics for a polyatomic molecule with the aid of which the vibration-rotation behavior of the molecule may be described.

An attempt is made to show in a straightforward way how a body-fixed frame may be constructed in classical and hence in quantum mechanics for a polyatomic molecule with the aid of which the vibration-rotation behavior of the molecule may be described.

Now a day centrifugal pumps are vital components of industries. Certainly, one of the most important specifications of centrifugal pumps are the performance curves. In the present work, performance curves of a centrifugal pumps are obtained by Computational fluid dynamics (CFD) and as an outcome, CFD results compare by practical curves. At the first step impeller and volute are designed with tw...

One can simplify the triad formulations of canonical gravity by abandoning any relation to a fixed coordinate system. That means in case of the adm formalism that one can determine the momentum by direct derivation of the Lagrange-3-form w.r.t the time-derivative of the triad-1-forms, thus the momentum is most naturally a 2-form. We apply this concept to the Palatini formulation where we can cl...

During a shift of gaze, an object can move along with gaze or stay fixed in the world. To examine the effect of an object's reference frame on spatial working memory, we trained monkeys to memorize locations of visual stimuli as either fixed in the world or fixed to gaze. Each trial consisted of an initial reference frame instruction, followed by a peripheral visual flash, a memory-period gaze ...

The report of the IAU Working Group on Nutation endorsed by Commissions 4, 8, 19 and 31 at the 1979 General Assembly points out that "... the complete theory of the general nutational motion of the Earth about its center of mass may be described by the sum of two components, astronomical nutation, commonly referred to as nutation, which is nutation with respect to a space-fixed coordinate syste...

We review some of the few available nonadiabatic calculations of dipole moments. We show that those carried out in a laboratory–fixed set of coordinate axes are bound to fail and discuss the more reasonable ones in a molecule–fixed reference frame. For completeness we also describe the standard Born–Oppenheimer calculations of dipole moments. We briefly address the experimental estimation of di...

Consider a 3-dimensional rigid body, B. Let C denote the point in B which is fixed during subsequent spherical motions. Choose a fixed reference frame, F whose origin lies at point C. To understand what happens to a rigid body during a spherical motion, select an arbitrary point, P0, in B. Let ~v0 denote the vector from the origin of this fixed reference frame to P0. I.e., ~v0 denotes the coord...

Consider a 3-dimensional rigid body, B. Let C denote the point in B which is fixed during subsequent spherical motions. Choose a fixed reference frame, F whose origin lies at point C. To understand what happens to a rigid body during a spherical motion, select an arbitrary point, P0, in B. Let ~v0 denote the vector from the origin of this fixed reference frame to P0. I.e., ~v0 denotes the coord...

Key Frame Selection The middle pane in Fig. 1 shows the three rectangular regions of fixed size around the eyes and mouth, selected on an example frame after aligning it with the reference frame f t0 (a neutral rest pose). These regions are used to build the LBP descriptors which are used to automatically find key frames depicting a similar expression as the reference frame. The right pane show...