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.

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...

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...

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 ...

KEY POINTS Reaching movements can be perturbed by vestibular input, but the function of this response is unclear. Here, we applied galvanic vestibular stimulation concurrently with real body movement while subjects maintained arm position either fixed in space or fixed with respect to their body. During the fixed-in-space conditions, galvanic vestibular stimulation caused large changes in arm t...

This thesis develops a nonlinear observer for the problem of pose estimation; that is, the determination of the position and attitude of a rigid body from sensor measurements. The observer is derived on the Special Euclidean group, SE (3), and exploits the natural Lie groups geometry of the space in the structure of the observer. The observer uses body fixed frame measurements of known landmark...

Metrics, which facilitate the measurement of parameters such as “distance” and “length” are used frequently in rigid body guidance problems. Commonly used metrics have a characteristic of being dependent on the choice of fixed or moving reference frame and the units used. Most motion synthesis algorithms require some notion of the “distance” between two desired locations. The metrics in Euclide...