Entire trajectory

Microwave interference (Doppler radar) techniques may be used to measure the velocity and displacement of the projectile in the barrel and its velocity over its entire trajectory. The basic system consists of a microwave transmitter... 

Comparison with results of traws-1,4-polybutadiene simulations confined to a channel shows that the correlation is much weaker in the case of the free chains. In particular, for the case of C50, less than 50% of the RIS transitions observed in the entire trajectory are identified as strongly coupled with next-nearest-neighbor transitions. For the C50 chain, the authors report the length of the dynamics run to be 3.7 ns Analysis of the entire data set of more than 2000 isomers reveals that on time scales of 0.1 ns or longer, an independent bond approximation reproduces the results of the molecular dynamics reasonably well. Analysis of shorter time simulations reveals higher mobility as a consequence of bond correlations that are important at these short time scales. 

So time scales with the scaling factor. Without belaboring the point with more complicated equations, it can be shown that for scaled guns with scaled propellants as well as scaled bullets, the muzzle velocities would be equal. Geometrically similar scaled bullets with equal mass densities have the same drag coefficients. It will be shown later that the entire trajectory is scaled such that velocity loss is equal over scaled distances. 

In the Section III.I, the watershed of the inherent structures was analyzed so as to find the transition region at the onset of the melting. The results show that the trajectories across the cells of class 1 are only about 10% of the entire trajectories that passed through the watershed. In contrast, the cells of classes 2 and 3 have a relatively high rate. In order to identify the transition region more clearly, Lindemann s was calculated again with a modified PES that is the sum of the original PES and an additional potential. The additional potential (U) used here is an exponential function whose center (r0) is on either of the stationary points as... 

The above algorithm for choosing the complex time path applies to non-reactive A + BC collisions, collinear or three-dimensional, throughout the entire trajectory. It is currently being used, for example, in the partial averaging calculations described in the previous section. 

Molecular dynamics simulations [69] of citric acid in water at room temperature do show intermolecular hydrogen bonds to the solvent molecules along the entire trajectory [54]. To observe a gauche/trans-transition (T3) within a time-frame of a few 100 ps, the simulation temperature has to be elevated. Computational studies including a molecular environment capable of forming hydrogen bonds clearly are more relevant than gas-phase calculations in the search for biologically active conformations. 

Even those reactions which remain on the lower surface for the entire trajectory exhibit a variety of interesting behaviour. In the same quasiclassical trajectory calculations on this system [52], we identified a substantial difference in the behaviour of those trajectories on the lowest surface which went deep into the H-O-H potential minimum (below an energy of -8.0 eV with respect to the reagents) and those which avoided it or went below this energy only once. The former yielded products having a substantially lower vibrational excitation than the latter. 

Integrating this expression from the distance of closest approach to infinity (this gives half the total difference in phase for the entire trajectory this is the convention for phase shift) gives... 

Shinoda Y, Sugihara I, Wu HS et al (2000) The entire trajectory of single climbing and mossy fibers in the cerebellar nuclei and cortex. Prog Brain Res 124 173-186... 

To find a joint trajectory that approximates the desired path closely, the Cartesian path points are transformed into N sets of joint displacements, with one set for each joint. Application of Bezier polynomial will provide trajectories that are smooth and have small overshoot of angular displacement between two adjacent knot points. The continuity conditions for joint displacement, velocity, and acceleration must be satisfied on the entire trajectory for the Cartesian robot path. 

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