Impulse of force

The procedure Merge transforms the internal displacement coordinates and momenta, the coordinates and velocities of centers of masses, and directional unit vectors of the molecules back to the Cartesian coordinates and momenta. Evolve with Hr = Hr(q) means only a shift of all momenta for a corresponding impulse of force (SISM requires only one force evaluation per integration step). 

The vertical spring and mass is an example of a stable system and by definition this means that an arbitrary small external force does not cause the mass to depart far from the position of equilibrium. Correspondingly, the mass vibrates at small distances from the position of equilibrium. Stability of this system directly follows from Equation (3.102) as long as the mechanical sensitivity has a finite value, and it holds for any position of the mass. First, suppose that at the initial moment a small impulse of force is applied, delta function, then small vibrations arise and the mass returns to its original position due to attenuation. If the external force is small and constant then the mass after small oscillations occupies a new position of equilibrium, which only differs slightly from the original one. In both cases the elastic force of the spring is directed toward the equilibrium and this provides stability. Later we will discuss this subject in some detail. 

The displacement response function x t, f) characterizes the average displacement (x(t) — x(to)) at time t, due to a unit impulse of force taking place at a previous time t < t. Is is easily deduced from the equation of motion (61), in which one adds to the random force F(t) a nonrandom force proportional to 5 (t — t ). One thus gets... 

The ballistic mortar suitable for the determination of the impulse of force at the explosive surface, applied in the former Soviet Union, is shown in Figure 5.9. 

The derivation of the mollified impulse method in [7] suggests that the same integrator be used for the auxiliary problem as that used for integrating the reduced primary problem M d fdt )X = F X) between impulses. Of eourse, Ax(x) is also needed. For the partitionings + j/aiow typically used in MD, this would lead unfortunately to a matrix Ax(x) with a great many nonzeros. However, it is probably important to take into account only the fastest components of [7]. Hence, it would seem sufficient to use only the fastest forces jjj averaging calculation. 

We derive the concept of the dynamic efficiency of the air curtain, E, which is equivalent to the ratio between aerostatic pressure forces affecting the gate aperture and the doubled initial impulse of the air curtain jets ... 

The forcing function of transform A is an impulse of magnitude K. The response to... 

Ya.B. Zel dovich, M.A. Rivin D.A. Frank-Kamenetskii, "Impulse of Reactive Force of Solid Propellant Rockets , CFSTI, Springfield, Va (1966) 194pp... 

Impulse (or momentum), in the physical sense, may be defined as the product of force and the time during which it acts... 

The momentum of the mass flow into the front is zero, because the medium is initially at rest the momentum of the medium leaving the front with a velocity, u, is pQUudt, and this increase of momentum must equal the impulse of the net force per unit area of the front, that is of the difference in pressure in the shock and in the medium at rest, (p-pQ)dt. Thus ... 

Impulse of a Primer. When a primer is fired, the force of detonation or length of spit is called impulse. It is measured by the maximum displacement of a mercury column resulting from the firing of the primer in an apparatus shown in Fig 15, p 50 of T.C. Ohart, Elements of Ammunition, J. Wiley, NY (1946)... 

After the pressure at the piston returns to zero, the gas is not acted upon by any external forces since the pressure in the cold gas is equal to zero both at x — —oo (in the limit at the boundary of dispersion), and at x — oo (x > X is sufficient) in the cold gas. In the motion, therefore, the total momentum of the gas, f pudx, is conserved. This momentum is equal to the pressure impulse of the piston,... 

For P increasing according to this law, in the limit, the impulse of the external force causing the motion (the impact impulse) I goes to zero I ss Pt ss t1/5. Consequently, the impulse equation for self-similar motion is written thus ... 

The central point within our consciousness, our "spirit" in the hermetic sense, can now be seen as an entity that can work to control quantum probabilities. To our "spirits" our brain is a quantum sea providing a rich realm in which it can incarnate and manifest patterns down into the electrical/chemical impulses of the nervous system. (It has been calculated that the number of interconnections existing in our brains far exceeds the number of atoms in the whole universe - so in this sense the microcosm truly mirrors the macrocosm ). Our "spirit" can through quantum borrowing momentarily press a certain order into this sea and this manifests as a thought, emotion, etc. Such an ordered state can only exist momentarily, before our spirit or point of consciousness is forced to jump and move to other regions of the brain, where at that moment the pattern of probability waves for the particles in these nerve cells, can reflect the form that our spirit is trying to work with. 

We note from Fig. 9 that the individual bonded and nonbonded contributions to t — 22, as they vary with p, are approximately equal in absolute value although opposite in sign. A possible heuristic picture for this behavior is based on Fig (8a) because of the short range and strongly repulsive character of u b, a nonbonded interaction has the character of a classic collision—the duration of an individual interaction is very short. As a result, the impacted atom (fl in Fig. 8a) moves little and the resultant of the impulsive compressive forces in its bonds to oq and a2 balance that exerted by x ( on [>. However, a collision in the configuration shown in Fig. 8b would contribute an impulsive tensile force to its bonds, but a collision between y ( and fi in that configuration is less likely because of steric shielding and, as verified in simulations, occurs less frequently. 

Therefore ve = u + Au -z and is the velocity of the ejected combustion gases relative to the rocket. Here the force (dm/df)ue corresponds to the thrust Fimpulse, which originates from the impulse of the system ... 

We begin with an abstract of the physics that underlies the kinetics of bond dissociation and structural transitions in a liquid environment. Developed from Einstein s theory of Brownian motion, these well-known concepts take advantage of the huge gap in time scale that separates rapid thermal impulses in liquids (< 10 s) from slow processes in laboratory measurements (e.g. from 10 s to min in the case of force probe tests). Three equivalent formulations describe molecular kinetics in an overdamped liquid environment. The first is a microscopic perspective where molecules behave as particles with instantaneous positions or states x(t) governed by an overdamped Langevin equation of motion,... 

Consider an inelastic collision between two smooth identical spherical particles 1 and 2, of mass m and diameter dp = d 2 [32] [60]. If J12 is the impulse of the force exerted by particle 1 on particle 2, the linear momentum balances over a collision relate the velocity vectors of the center of each sphere just before and after the collision through ... 

It is required that the component of the relative velocity perpendicular to the apse line should be unchanged in a collision, thus the impulse J12 must act entirely in the k direction. On this demand, J12 can be determined from (4.21), (4.22) and (2.123). The impulse of the force exerted by particle 1 on particle 2 is given by ... 

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