Special Theory of Relativity in Hyperbolic Functions

The purpose of the essay is to show the advantages of hyperbolic functions in restricted relativity. Based on the work of Fontené and others, the author has further developed the use of rapidities in place of velocities and has introduced festinations in place of accelerations. A simple universal distortion factor is deduced in hyperbolic notation, and symmetrical expressions are derived for mechanical force, momentum, and energy. The theories of aberration of light and of Fizeau's experiment are used further to demonstrate the advantages of hyperbolic functions in relativity. The invariance of Maxwell's equations for the two observers in relative motion is proved in two different and independent ways: (a) by the method of paired functions, and (b) by using divergence and curl in a semihyperbolic four-dimensional space. A list of references to books on restricted relativity and to the author's previous contributions on the subject is appended.