Abstract
The natural meaning attached to the resultant of two continuously differentiable motions (flows) is the motion obtained by adding their velocities, but when velocities are not meaningful, there is no predetermined idea of what a resultant ought to be. The present work provides a pair of natural axioms to be satisfied by any motion called a resultant, and it is shown that for motions that are in some sense parallel, this definition of a resultant is the most general one possible.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anatole Beck,Addition of Generalized Velocities, presented at the International Congress of Mathematicians, Moscow, 1966.
Anatole Beck, Uniqueness of Flow Solutions of Differential Equations,Springer-Verlag Lecture Notes in Mathematics, vol. 318.
Anatole Beck, Continuous Flows in the Plane,Grundlehren der Mathematischen Wissenschaften, vol. 201, Springer-Verlag.
Anatole Beck, Private communication.
Jonathan Lewin, Reparametrization of Continuous Flows,PhD Dissertation, University of Wisconsin, 1970.
Myrtle Lewin, Algebraic Combinations of Continuous Flows,PhD Dissertation, University of Wisconsin, 1970.
Coke S. Reed, The Addition of Dynamical Systems,Mathematical Systems Theorv 6(3) (1972), 210–220.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lewin, J., Lewin, M. A uniqueness theorem on the resultant of two non-differentiable motions. Math. Systems Theory 9, 241–247 (1975). https://doi.org/10.1007/BF01704022
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01704022