Mathematical extension of special relativity into three-dimensional internal acceleration

Abstract

The special theory of relativity (STR) has already been expanded onto normal and binormal subcomponents of an internal acceleration visible within 3D trihedron moving in Frenet frame (T,N,B) along the trajectory curve, in addition to the constant tangential speed of classical STR. Now the STR is extended into tangential, normal, and binormal subcomponents of total internal acceleration in the (moving, curving, and twisting/torsing) trihedron via the varying total internal speed that is extracted from the external speed, which is allowed to vary now with the extended proper/moving time in the external length-based space within operationally imaginary but physically real internal domain of the elapsing proper/moving time. The temporarily emerging extra internal acceleration also implies temporarily arising extra internal forces that could affect airplanes in flight just as they affect the moving zero-dimensional mathematical point. For even an invisible, i.e., mathematically imaginary, force is still physically real active force.