If, without the action of force, the particle moved not in a straight line, but along a helical line of an infinite cylinder, where the momentum of the particle is given by the number of revolutions per unit of time, then the force of gravity could be represented as a local stretching of the cylinder, and the electric force of the Coulomb as a local torsion of the cylinder. The book below shows how to extend this formalism to all the forces of nature.
Research Proposal MATHEMATICAL NOTES ON THE NATURE OF THINGS
Dear Igor, although I haven't had time to work through your mathematical notes, in order to start discussions it could help to recast the statements of the abstract (e.g. 'without the action of force' vs. ... moved not in a straight line, etc.)... There is also known analytic background from the theory of screws (R.S.Ball; article series at the end of 19th century and two books 1876/1900) as well as Zindler's line geometry to provide an analytical basis which is better suited than geometric/Clifford algebra or comparing to vector calculus. As starting point, based on Plücker's work, Lindemann (a student of Clebsch and F. Klein) has worked it out in his PhD thesis (1873), later used by Ball and Lie in his book on contact interactions (1896). The helical line you've mentioned is included as a special case, the complete description (nowadays one would denote them as kinematical irreps) has been given by E. Study in terms of Dynamen and Somen, i.e. the S^7 with all the analytical and topological (Hopf) stuff and the bunch of different reps known and used today...
Rolf Dahm
Dear Rolf,
The fact is that we mean helices not in the physical 3-dimensional Euclidean space, but in the 4-dimensional metaphysical space. In general, this question is in conjunction with another question.
https://www.researchgate.net/post/What_does_a_4-dimensional_Euclidean_space_look_like_from_the_point_of_view_of_a_3-dimensional_observer
As for the predecessors, thank you for remembering them.
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