Annex X.7 – ABSOLUTE AND RELATIVE FLUXES

Let us take a material system MS₁, with the spatial position , which is momentarily considered as invariant against an external RS_e. In such conditions, any flux defined against RS_e and which intersects RBS of a MS₁ is considered (for this MS) as an active flux, because it is able to generate an action on the system. The intensity of these fluxes is equal with the attribute amount which is carried in a time unit through a motionless imaginary surface, normal on the flux line. In case of our material system, the agent fluxes are decomposed on RBS into trafluxes and refluxes, and the traflux enters into the system by modifying its internal state first, and then, its external one. The traflux intensity is the integral on RBS of its normal and tangential component, determined into the time unit as well; the normal component shall provide the normal traflux (component T of the traflux) and the tangential one, shall provide the tangential traflux (component R of the traflux). The fluxes distribution is also similar in relation with the internal RS (which shall be referred to as RS_i) of MS₁, with just an origin displacement.

All goes well as long as MS₁ stands still. But, what it happens if becomes variable, which means that MS₁ shall be moving with the velocity (determined against the same external RS_e)? It is natural to presume that all the distributions of the fluxes which are incident on RBS of MS₁ would be changed because their transfer rates by means of RBS shall be vectorially composed on RBS of MS₁, with velocity , and even more, all the motionless material systems (against the same external RS_e) which are placed on the motion direction of MS₁ shall become fluxes (for MS₁), but this time, they are defined against the internal RS_i of MS₁, and they are fluxes which shall move with the velocity -against RS_i. If the fluxes which were determined against an external RS_e (considered as an absolute RS) may be called absolute fluxes, the fluxes whose transfer rate is determined against an internal RS_i of a MS shall be called relative fluxes against that particular internal RS_i.

But, my dear reader, we have seen that any material flux which is incident on a RBS of a MS and which has a component sent inward (traflux), regardless of its name, is an agent flux, which generates an action on that MS; similarly, a relative (at the internal RS of a MS) flux can be an agent flux for that MS, the action produced by it on a driven MS has a special name even since the Newton’s time – that is reaction.

Otherwise speaking, the reaction is a response of a driven MS, to the action of an external flux, response which consists in the state modification produced on the agent flux by the reaction flux¹00 generated by the driven object, that is a flux which occurs as a result of a relative motion.

Let us assume that we have two material systems MS₁ and MS₂ which deploy an even motion (with constant velocity against an external RS_e), with velocity , respectively . The two velocity rates are given by the following relations:

(X.7.1.a)

and:

(X.7.1.b)

where and are the position vectors of the two MS, and , and dt are elementary variations under the meaning given by the objectual philosophy (not in the sense of the classic differential calculus, see the chapters 2, 3, 4 and the annex X.3). The internal references T of the two MS have a relative position one against the other:

(X.7.2.a)

and:

(X.7.2.b)

If the relative distance (position) vectors are coplanar with the vectors and (which means that the mixed product of the three vectors is null), then, the fluxes T generated through the translation motion of the two bodies can be intersected one another¹01, which means that the two MS shall interact (by means of collision) in a future moment. In this case, the relative transfer rates¹02 of the two fluxes shall be:

(X.7.3)

namely, in case of the relative fluxes between the elements of a MS couple, their relative transfer rates shall be always equal and shall have an opposite sign¹03, regardless of the absolute values of the two velocity rates and regardless of their evaluation moment.

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INDEX

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