The links below are to the Sections of the paper on the simplified mathematical representation of The Special Theory of Relativity.

This paper published in the online Journal Apeiron Vol.10 (4). See Links page.

Introduction - The first section contains a title page, a brief abstract, a description of the mathematical nomenclature used, a contents page and the main introduction.

The Relativistic Domain - The second section defines the relativistic Domain D₀, the space-time in which the development is accomplished. It establishes the criteria for existence within the Domain, and its general characterisation.

Rectilinear Motion - The third section deals with the mechanics of simple rectilinear motion within D₀. The well known relationships for all three variants of relativistic mass, and the equation of relativistic motion are developed. This is followed by considerations of the accelerating force, and both kinetic and total energies.

Curvilinear Motion - The fourth Section applies the foregoing mathematical techiques to the problem of relativistic curvi-linear motion. Some new relativistic relationships are developed.

Planar Orbital Motion - As a final example, this section applies the techniques to the development of relativistic planar orbital kinematics. The equation of the orbit is firstly developed, and then solved for the classic example of two oppositely charged particles, to reveal the precessing orbit of the smaller particle about the larger.

Conclusions - Brief concluding remarks together with the introduction of the Appendix.

Appendix A - The first Appendix demonstrates that the space-time Domain D₀ is equivalent to Pseudo-Euclidean Space Time by developing, from first priciples, the relationship between the spacial and temporal axes of D₀, and those associated with a point moving with a constant rectilinear velocity within D₀. This relationship is seen to be identical to the Lorentz transformations of the Special Theory.

Appendix B - The second Appendix reduces selected derivations to their equivalent expressions in classical analysis.

References

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