scholarly journals Rate of Change of Momentum

1910 ◽  
Vol 6 ◽  
pp. 66-71
Author(s):  
P. Pinkerton

The object of this note is to suggest how Newton's Laws of Motion may be approached explicitly by means of rate of change of momentum. It will be seen that the term “force” is not made prominent at the expense of the notion of rate of change of momentum. Once the student believes that rate of change of momentum is a vital aspect of stopping or starting the motion of a body, he is not inclined to overestimate his knowledge of “force” apart from the rate of change of momentum which accompanies it. Since students of ordinary endowment learn to observe things before words, we begin with some common examples. As for the term “momentum,” it is sufficient to begin by saying that

1988 ◽  
Vol 11 ◽  
pp. 137-149 ◽  
Author(s):  
S. Shabtaie ◽  
C. R. Bentley ◽  
R. A. Bindschadler ◽  
D. R. MacAyeal

Recent airborne radar sounding has made it possible to map accurately three of the West Antarctic ice streams that flow into Ross Ice Shelf. In previous work we have shown that ice streams A and Β have negative mass balances, whereas inactive Ice Stream C has a strongly positive balance. In this paper we examine in more detail the balance of ice streams A and Β by constructing several gates across them where velocities and ice thicknesses have been measured. We then examine the net fluxes in blocks of the ice streams delimited by successive pairs of gates.Ice Stream A as a whole is apparently discharging more ice than is being accumulated in the catchment area, and currently thinning at the rate of 0.08 ± 0.03 m a−1. The situation on Ice Stream Β is more complex. We have calculated separately the fluxes from tributary ice streams Bl and B2, and examined their individual fluxes within Ice Stream Β by tracing the suture zone between them down-stream of their confluence. The flow band that is the farthest up-stream (girdle), encompassing both Ice Stream Bl and Ice Stream B2, shows a strongly negative net flux that we attribute to lateral and headward expansion of the ice streams within the band. Such expansion can occur by lateral movement of an ice-stream boundary, by temporally accelerating ice flow at the head of the ice stream, or by activation of formerly slowly moving “island” or “peninsula” ice.The imbalance in this flow band, 8 ± 2 km3 a−1 (equivalent mean rate of change in ice thickness, is nearly half of the total excess outflow for the Ice Stream Β system (20 ± 4 km3 a−1), — the remainder is mostly the difference between flow through the uppermost gate and mass input to the catchment area .When for the whole of Ice Stream Β is plotted against the distance along the entire Ice Stream B, the overall pattern appears to be of mild thinning in the catchment, intense thinning in the girdle, and thickening in the main body of the ice stream, which decreases with distance from the girdle. This global behavior is suggestive of a major transient response, resulting from either a change in the internal dynamics or an internal adjustment to a change in the external forcings. We argue that there are a number of conditions which could lead to this type of response pattern. One possibility is a surge. Although the distribution of the changes in thickness is one characteristic of a surge, we caution that this alone is not sufficient to classify the behavior as a surge. Several other possibilities that support a picture of Ice Stream Β as a system in the process of dynamic change and in unsteady state are discussed.At present, Ice Stream C and its catchment area are thickening over their entire area The present surface elevation does not suggest that Ice Stream Β has captured part of Ice Stream C. Moreover, the shut-down of Ice Stream C and the large mass imbalance of Ice Stream Β are not related.


Author(s):  
Tony Bridgeman ◽  
P. C. Chatwin ◽  
C. Plumpton

1959 ◽  
Vol 55 (2) ◽  
pp. 177-180 ◽  
Author(s):  
R. A. Sack

1. Introduction. Ledermann(1) has treated the problem of calculating the asymptotic probabilities that a system will be found in any one of a finite number N of possible states if transitions between these states occur as Markov processes with a continuous time parameter t. If we denote by pi(t) the probability that at time t the system is in the ith state and by aij ( ≥ 0) the constant probability per unit time for transitions from the jth to the ith state, the rate of change of pi is given bywhere the sum is to be taken over all j ≠ i. This set of equations can be written in matrix form aswhere P(t) is the vector with components pi(t) and the constant matrix A has elements


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