In all cases this is effected by allowing the constant velocity parameter c to become infinite. Only the main equations for which a classical equivalent exists is so treated. Trivial examples will be ignored unless a special condition is implied.

(i) Eq. (2.5), the temporal rate. When c ®

(B1)

Hence in classical theory the proper time of a moving body is identical to the time in D₀, Pseudo-Euclidean Space-Time.

(ii) Eq. (2.6), Existence Velocity. When c ®

(B2)

Hence temporal velocity in classical studies is "infinite". Existence velocity does not exist in classical mechanics, and temporal velocity in such studies, is therefore a meaningless concept because it implies that time passes infinitely quickly. Where a concept does not exist in classical mechanics etc, relativistic reduction generally results in an infinite or zero value.

(iii) Eqs. (3.6) and (3.9), Rest, Energy and Inertial Mass. When c ®

(B3)

Thus rest, energy and inertial mass are identical in classical mechanics. Hence any reference to inertial mass in such studies is meaningless. Consequently, as is evident from Eq (3.7), when c ®

(B4)

(iv) Eq (3.19), Kinetic Energy. To determine the classical expression for kinetic energy directly from (3.19) would be incorrect because (3.19) is a relationship in matter energy, a concept that does not exist in classical mechanics. The correct procedure is first to insert (3.6) into (3.19) and expand the result binomially to yield

(B5)

from which, when c ®

(B6)

the classical result.

(v) Eq. (4.14), the acceleration vectors along the co-ordinant axes, when c ®

(B7)

and clearly therefore the force and acceleration vectors are coincident.

(vi) Eq. (4.15), the mass on each co-ordinant axis, when c ®

(B8)

(vii) Eq. (4.17), Angular relationship between the acceleration vector and the X axis, when c ®

(B9)

which confirms the result at (B7).

(viii) Eqs. (4.18) and (4.21), accelerations along and normal to the velocity vector, when c ® .

and

(B10)

so that from (B7) and (B10)

(B11)

which now also shows that the force, acceleration and velocity vectors are co-incident.

(ix) Eq. (5.5), general curvi-linear equation of motion, when c ®

(B12)

the classical equation in mechanics.

(x) Eq. (5.24), equation of planar motion in the proper time, when c ®

(B13)

the classical equation in mechanics.

(xi) Eq. (5.29), the equation of a central orbit, when c ®

(B14)

where

the classical equations in mechanics.

(xii) Eq. (5.37), the equation of a central orbit trajectory, when c ®

(B15)

which is clearly the equation of a simple conic section. The semi-latus rectum and eccentricity are

and

(B16)

These are again the classical results.

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