Restoring force, definition

J is applied. A crash test sequence is shown in Fig. 8.33. The profile is bent up to the maximum deformation of about 107 mm. Subsequently the test sled was pushed backwards by the restoring force of the profile due to the elastic strain of the profile. This sequence clearly demonstrates the integrity of the profile and especially of the in situ joined zone, which is definitely not the weak point of the chosen profile geometry and material under the given load conditions. 

The relative positions of potential curves are illustrated in Fig. 1. The restoring forces have their origin from the purely quadratic terms in the expansion series of Eq. (1), however, since the Hamiltonian in the derivatives, by definition, describes only the electronic energy they do not entirely correspond to the quadratic terms of Eq. (9) because the latter include also repulsions of the nuclear cores. On the other hand, when considering differences of restoring forces between excited and ground states by which contributions due to core repulsions are cancelled, the result can be related to corresponding term differences of Eq. (1) if, e.g., expectation values as... 

The expression based on normal coordinates by definition involves no interaction force constant. However, in general, for any other set of coordinates an interaction force constant iiust be included to take account of the effect of displacement in one coordinate upon the restoring force in the other. For bond coordinates we have... 

The behaviour of materials of low relative molecular mass is usually discussed in terms of two particular types of ideal material the elastic solid and the viscous liquid. The former has a definite shape and is deformed by external forces into a new equilibrium shape on removal of these forces it reverts instantaneously to its original form. The solid stores all the energy that it obtains from the external forces during the deformation, and this energy is available to restore the original shape when the forces are removed. By contrast, a viscous liquid has no definite shape and flows irreversibly under the action of external forces. 

By definition, ion pairs are low energy assemblies, and removal of one of the ion pair partners after templated synthesis places an interlocked structure in a high energy state. Restoration of the ion pair interaction is highly favorable and produces a spring-like driving force that can be exploited for dynamic molecular functions. 

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